I. Very Short answer type questions:
1. What is the approximate value of g?
Ans. The approximate value of g is 9.8 m/s2.
2. Name the scientist who proved for the first time that objects move with constant speed when no force acts on them.
2. Name the scientist who proved for the first time that objects move with constant speed when no force acts on them.
Ans. Newton.
3. When a body is said to be in equilibrium?
3. When a body is said to be in equilibrium?
Ans. A body is said to be in equilibrium when it is at rest or moving with uniform velocity or uniform acceleration which is due to the forces acting on the body are equal and opposite.
4. Define the resultant force.
Ans. The resultant force is a net force acting on a body along with its direction. When a body at rest or moving with a uniform velocity, the net force has to be zero.
5. What is the S.I unit of force?
Ans. The S.I unit of force is Newton (N).
6. Is momentum a scalar or vector quantity?
Ans. Momentum is a vector quantity because momentum has both direction and magnitude.
7. Write the expressions of force and weight.
Ans. Expression of force and weight is F = mg
Where F is the force, m is the mass Ang g is the acceleration due to gravity.
8. In a tug of war, the rope does not move in any direction. Why?
Ans. In a tug of war, the rope does not move in any direction because the forces acting on the body are equal and opposite which is called balanced force.
9. Define 1-Newton force.
Ans. 1-Newton force is defined as the amount of force that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
10. Define linear momentum.
Ans. The product of mass and velocity of a moving body is called linear momentum.
Momentum p = mv.
11. Write the expression and unit of momentum.
Ans. Expression of momentum p = mv (where = momentum, m = mass and v = velocity)
S.I unit of momentum is Kg m/s.
12. Name the force which is responsible for the change in position or state of an object.
Ans. An unbalanced force is responsible for the change in the position or state of an object.
13. Define Inertia.
Ans. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called the inertia.
14. What is the relation between inertia and mass?
Ans. The property of the inertia is because of the mass of the body. The greater the mass, the greater is the inertia of the body.
15. Which has the highest inertia solid made of aluminum, steel, and wood of the same shape and volume?
Ans. Steel has the highest inertia because the mass of steel is more than the aluminum and wooden solid because the greater the mass, the greater is the inertia of the body so.
16. Name the unbalanced force which slows down a moving bicycle when we stop paddling it.
Ans. The unbalanced force which slows down a moving bicycle when we stop paddling is the frictional force between the road and wheel of the bicycle acting opposite to the direction of motion.
17. Give one point of difference between a balanced and unbalanced force.
Ans. Balanced force - The net effect produced by a number of forces on a body is zero.
Unbalanced force - The net effect produced by a number of forces on a body is non zero.
18. Why does the sole of the shoe wear?
Ans. Sole of the shoe wear out due to the friction between the sole shoe and road.
19. A force is applied on a metal block lying on the floor in one direction. Still, the block does not move. Name the force which is balancing it.
Ans. A force is applied on a metal block lying on the floor in one direction still, the block does not move it because An equal and opposite frictional force between the metal block and floor balancing it.
20. Find the acceleration produced by a force of 12 N exerted on an object of mass 3 kg.
Ans. Given that F = 12 N, mass = 3 kg
F = ma
Acceleration (a) = F/m = 12/3 = 4 m/s2
21. Find the momentum of a man of mass 75 kg when he walks with a velocity of 2 m/s.
Ans. Given mass of man = 75 kg,
velocity v = 2 m/s.
Momentum = mv, where m = mass and
v = velocity.
Momentum = 75 x 2 = 150 kgm/s.
22. The mass of a body is doubled. How does its acceleration change under a given force?
Ans. We know that force F = ma. Therefore a = F/m
Here acceleration is inversely proportional to mass, so when the mass of a body is doubled its acceleration becomes half.
23. Write any two kinds of changes or effects of a force produces in a nonrigid body fixed at a position.
Ans. Two kinds of changes or effects of a force produce in a nonrigid body fixed at a position are change its shape and size.
24. When a carpet is beaten with a stick it releases dust. Explain why?
Ans. It is due to the inertia of rest in which when a carpet is beaten, the carpet comes in motion but the dust remains in the state of rest and leaves the carpet and fall down.
25. State an example, how force can change the velocity of a body?
Ans. By applying brakes we can slow down the car.
26. Why are the athletes in a high jump even made to fall either on a cushioned bed or on a sand bed?
Ans. To reduce the rate of change in momentum by increasing the time duration in which his feet come to rest and force exerted on his feet decreases and he is saved from getting hurt.
27. A ball is thrown vertically upwards. What is its momentum at the highest point?
Ans. When a ball is thrown vertically upwards, its velocity at the highest point becomes zero so its momentum will be zero.
28. Name the physical quantity which is measured by the rate of change of momentum.
Ans. Force.
F = (mv - mu)/t = m(v - u)/t = ma [ (v-u)/t =a ]
29. What is the physical quantity of inertia and its S.I unit?
Ans. The physical quantity of inertia is mass and the S.I unit is Kg.
30. During the game of table tennis, if the ball hits a player it does not hurt him. On the other hand, when a fast moving cricket ball hits a spectator it may hurt him. State the reason.
Ans. The momentum force is directly proportional to mass and the mass of a cricket ball is greater than the tennis ball, so the momentum of a cricket ball is larger than a tennis ball and hurts the spectators.
31. If the initial velocity is zero then the force acting is:-
(a) Retarding (b) Acceleration (c) Both (d) None.
Ans. (b) Accelerating.
32. A force is applied on a metal block lying on the floor in one direction. Still, the block does not move. Name the force which is balancing it.
Ans. The frictional force between the metal block and floor is balancing it.
33. Name the physical principle on which jet aircraft work.
Ans. Newton's third law is the physical principle on which jet aircraft work. According to Newton's third law, when jet air crafts exert force on the air, air gives equal and opposite reaction force on the jet, due to which jet aircraft can move in the forward direction.
II. Short answer type questions:
1. When we can say that the balanced or unbalanced force acts on an object?
Ans. When forces acting on a body from all sides are equal and opposite, they cancel the effect of each other, are known as a balanced force. On the other hand, when forces acting on a body are not equal and do not cancel each other are called unbalanced forces.
8. State an example, how force can change the velocity of a body? Write the type of force acting between moving body and floor.
Ans. According to the newtons 2nd law, F = ma, therefore, a force can cause acceleration on a moving body and acceleration means a change in velocity at constant rate i.e, a force can change the velocity of a body E.g., a moving ball comes to rest
The frictional force acting in the opposite direction of motion between moving body and floor.
9. (a) If action is always equal to the reaction, explain how a horse can pull a cart?
(b) Write the units of force and momentum.
Ans. (a) When a horse pushes the ground in the backward direction, the earth exerts a reaction force in the forward direction. The force exerted by the horse is action force and force exerted by the earth is reaction force. According to Newton's third law of motion action and reaction, forces are equal and opposite. With the help of the reaction force exerted by the earth, a horse can pull the cart.
(b) The unit of force is kg m/s2 or Newton N.
The unit of momentum is Kg m/s.
16. When a bullet is fired from a gun, the gun recoils. Why?
Ans. When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun. Since the gun has a much greater mass than the bullet, the acceleration of the gun is much less than the acceleration of the bullet.
4. Define the resultant force.
Ans. The resultant force is a net force acting on a body along with its direction. When a body at rest or moving with a uniform velocity, the net force has to be zero.
5. What is the S.I unit of force?
Ans. The S.I unit of force is Newton (N).
6. Is momentum a scalar or vector quantity?
Ans. Momentum is a vector quantity because momentum has both direction and magnitude.
7. Write the expressions of force and weight.
Ans. Expression of force and weight is F = mg
Where F is the force, m is the mass Ang g is the acceleration due to gravity.
8. In a tug of war, the rope does not move in any direction. Why?
Ans. In a tug of war, the rope does not move in any direction because the forces acting on the body are equal and opposite which is called balanced force.
Ans. 1-Newton force is defined as the amount of force that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
10. Define linear momentum.
Ans. The product of mass and velocity of a moving body is called linear momentum.
Momentum p = mv.
11. Write the expression and unit of momentum.
Ans. Expression of momentum p = mv (where = momentum, m = mass and v = velocity)
S.I unit of momentum is Kg m/s.
12. Name the force which is responsible for the change in position or state of an object.
Ans. An unbalanced force is responsible for the change in the position or state of an object.
13. Define Inertia.
Ans. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called the inertia.
14. What is the relation between inertia and mass?
Ans. The property of the inertia is because of the mass of the body. The greater the mass, the greater is the inertia of the body.
15. Which has the highest inertia solid made of aluminum, steel, and wood of the same shape and volume?
Ans. Steel has the highest inertia because the mass of steel is more than the aluminum and wooden solid because the greater the mass, the greater is the inertia of the body so.
16. Name the unbalanced force which slows down a moving bicycle when we stop paddling it.
Ans. The unbalanced force which slows down a moving bicycle when we stop paddling is the frictional force between the road and wheel of the bicycle acting opposite to the direction of motion.
17. Give one point of difference between a balanced and unbalanced force.
Ans. Balanced force - The net effect produced by a number of forces on a body is zero.
Unbalanced force - The net effect produced by a number of forces on a body is non zero.
18. Why does the sole of the shoe wear?
Ans. Sole of the shoe wear out due to the friction between the sole shoe and road.
19. A force is applied on a metal block lying on the floor in one direction. Still, the block does not move. Name the force which is balancing it.
Ans. A force is applied on a metal block lying on the floor in one direction still, the block does not move it because An equal and opposite frictional force between the metal block and floor balancing it.
20. Find the acceleration produced by a force of 12 N exerted on an object of mass 3 kg.
Ans. Given that F = 12 N, mass = 3 kg
F = ma
Acceleration (a) = F/m = 12/3 = 4 m/s2
21. Find the momentum of a man of mass 75 kg when he walks with a velocity of 2 m/s.
Ans. Given mass of man = 75 kg,
velocity v = 2 m/s.
Momentum = mv, where m = mass and
v = velocity.
Momentum = 75 x 2 = 150 kgm/s.
22. The mass of a body is doubled. How does its acceleration change under a given force?
Ans. We know that force F = ma. Therefore a = F/m
Here acceleration is inversely proportional to mass, so when the mass of a body is doubled its acceleration becomes half.
23. Write any two kinds of changes or effects of a force produces in a nonrigid body fixed at a position.
Ans. Two kinds of changes or effects of a force produce in a nonrigid body fixed at a position are change its shape and size.
24. When a carpet is beaten with a stick it releases dust. Explain why?
Ans. It is due to the inertia of rest in which when a carpet is beaten, the carpet comes in motion but the dust remains in the state of rest and leaves the carpet and fall down.
25. State an example, how force can change the velocity of a body?
Ans. By applying brakes we can slow down the car.
26. Why are the athletes in a high jump even made to fall either on a cushioned bed or on a sand bed?
Ans. To reduce the rate of change in momentum by increasing the time duration in which his feet come to rest and force exerted on his feet decreases and he is saved from getting hurt.
27. A ball is thrown vertically upwards. What is its momentum at the highest point?
Ans. When a ball is thrown vertically upwards, its velocity at the highest point becomes zero so its momentum will be zero.
28. Name the physical quantity which is measured by the rate of change of momentum.
Ans. Force.
F = (mv - mu)/t = m(v - u)/t = ma [ (v-u)/t =a ]
Ans. The physical quantity of inertia is mass and the S.I unit is Kg.
30. During the game of table tennis, if the ball hits a player it does not hurt him. On the other hand, when a fast moving cricket ball hits a spectator it may hurt him. State the reason.
Ans. The momentum force is directly proportional to mass and the mass of a cricket ball is greater than the tennis ball, so the momentum of a cricket ball is larger than a tennis ball and hurts the spectators.
31. If the initial velocity is zero then the force acting is:-
(a) Retarding (b) Acceleration (c) Both (d) None.
Ans. (b) Accelerating.
32. A force is applied on a metal block lying on the floor in one direction. Still, the block does not move. Name the force which is balancing it.
Ans. The frictional force between the metal block and floor is balancing it.
33. Name the physical principle on which jet aircraft work.
Ans. Newton's third law is the physical principle on which jet aircraft work. According to Newton's third law, when jet air crafts exert force on the air, air gives equal and opposite reaction force on the jet, due to which jet aircraft can move in the forward direction.
II. Short answer type questions:
1. When we can say that the balanced or unbalanced force acts on an object?
Ans. When forces acting on a body from all sides are equal and opposite, they cancel the effect of each other, are known as a balanced force. On the other hand, when forces acting on a body are not equal and do not cancel each other are called unbalanced forces.
2. Define Balanced and unbalanced force.
Ans.When two equal forces acting on a body in the opposite direction, do not change the state of rest or motion of the object. These forces are called balanced forces.
When two opposite forces of different magnitudes acting on a body, the body would begin to move in the direction of the greater force. These two forces are called the unbalanced force acts in the direction the body moves. An unbalanced force acting on an object brings it in motion.
3. Define force and write the types of forces?
Ans. a force is any interaction that, when unopposed, will change the motion of an object. Its S.I unit is Newton N and represented by the symbol F.
There are two types of force, contact force, and non-contact force. Examples of contact force: gravitational force and electrostatic force.
Examples of non-contact force: Frictional force and muscular force.
Ans.When two equal forces acting on a body in the opposite direction, do not change the state of rest or motion of the object. These forces are called balanced forces.
When two opposite forces of different magnitudes acting on a body, the body would begin to move in the direction of the greater force. These two forces are called the unbalanced force acts in the direction the body moves. An unbalanced force acting on an object brings it in motion.
3. Define force and write the types of forces?
Ans. a force is any interaction that, when unopposed, will change the motion of an object. Its S.I unit is Newton N and represented by the symbol F.
There are two types of force, contact force, and non-contact force. Examples of contact force: gravitational force and electrostatic force.
Examples of non-contact force: Frictional force and muscular force.
4. On what factors does the momentum of a body depend?
Ans. Momentum is the product of mass and velocity.
Momentum p = mv
So two factors of momentum are mass and velocity.
5. What is the magnitude and direction of resultant force if two forces of magnitude F each act at a point toward the right?
Ans. The resultant force is the sum of two forces.
Therefore F + F = 2F and direction is towards the right.
6. Define the conservation of linear momentum.
Ans. The sum of momenta of the two objects before the collision is equal to the sum of momenta after the collision, provided there is no external unbalanced the force acting on them. This is known as the law of conservation of momentum.
Or The total momentum is conserved during the interaction.
7. State the meaning of recoil of the gun.
Ans. When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun.
8. Give an example where two equal and opposite forces do not form an action-reaction pair.
Ans. When a body moves in a circular path, two forces act on it and they are the centripetal and centrifugal force which is equal and opposite. These are not action and reaction force because action and reaction always act on two different objects
9. State Newton's first law. Why is it known as the law of inertia?
Ans. According to Newton's first law of motion, if a body is in rest, it will remain in the state of rest, and if it is in a state of motion, it will remain moving in the same direction with uniform velocity unless an external force is applied on it.
It is known as the law of inertia because this property of an object by virtue of which it neither changes its present state nor it tends to change the present state, is called inertia.
10. Differentiate between mass and weight?
Ans. Differences between mass and weight are:
(i) Mass of a body is a measure of the quantity of matter contained in the body where weight is the force by which the earth attracts the body.
(ii) Mass is a scalar quantity, weight is a vector quantity.
(iii) It is constant for the body and does not change by changing the place of the body, weight is not constant but varies from place to place
11. What are the factors on which inertia depends?
Ans. The factor on which inertia depends directly, are mass and acceleration.
The greater the mass, the greater is the inertia of the body.
More the mass of a body more difficult it is to move the body from rest or to stop the body if it is initially moving.
Similarly the greater the acceleration, the greater is the inertia of the body.
12. State Newton's second law of motion.
Ans. The first law of motion indicates that when an unbalanced external force acts on an object, its velocity changes, that is the object gets an acceleration and the acceleration of an object depends on the force applied to it. Newton's second law of motion gives the quantitative value of force.
Therefore F = ma.
13. State Newton's second law in terms of momentum.
Ans. According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the force applied on it and the change in momentum is in the direction in which the force is applied.
14. Explain Newton's first law in terms of the second law.
Ans. The first law of motion can be mathematically stated from the mathematical expression for the second law of motion.
F = ma or F = m(v − u)/ t
or F= (mv – mu)/t .That is when F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest. This is the newtons second law.
15. A book kept on a table. There are two forces on the book -normal force in the upward direction and gravitational force in a downward direction. Is this pair of force is an action-reaction pair? Explain your answer.
Ans. No, because according to the third law of motion which states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These forces act on different objects and never on the same object and the book is the only object on which both forces act.
16. Define inertia. What are the two types of inertia?
Ans. All objects resist a change in their state of motion. In a qualitative way, the tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia.
There are two types of inertia: The motion of inertia and the rest of inertia.
17. If an object experiences a non zero external unbalanced force. Is it possible for the object to be traveling with a non zero velocity? State your answer.
Ans. Yes, Is it possible for the object to be traveling with a non zero velocity if the resistance between air and the moving object is zero and the object moving with uniform motion because the external unbalanced force is needed to initiate the motion.
18. karate player can break a pile of tiles in a single blow with his hands. How?
Ans. Karate player moves his hand with high speed due to which momentum force increases and strikes the pile with his hand very fast. Thus the entire momentum of the fast-moving hand is reduced to zero in a very short time, due to this, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for breaking the pile of tiles.
19. Raju is having three solid blocks of the same size and shape and made up of steel, wood, and plastic. Which one of these will have the highest inertia. Give a reason for your choice.
Ans. Solid blocks made up of steel will have the highest inertia, because steel has more mass and inertia depends on mass directly. Therefore greater the mass, the greater is the inertia of the object.
III. Long answer type questions:
1.Define (i) Force (ii) Contact force (iii) Non contact force (iv) Frictional force.
Ans. (i) Force - Force is an external cause that can change the state of rest or the state of motion of an object. It is a vector quantity and the S.I unit is N.
(ii) Contact force - A force exerted on a body when it is in contact with the body is called contact force. Example - Push or pull, Muscular force, etc.
(iii) Non-contact force - A force exerted on a body without any contact with two bodies is called contact force. Example - Gravitational force. Electrostatic force etc.
(iii) Frictional force - Frictional force is the force caused by the relative motion of two surfaces that come in contact with each other.
Ans. Momentum is the product of mass and velocity.
Momentum p = mv
So two factors of momentum are mass and velocity.
5. What is the magnitude and direction of resultant force if two forces of magnitude F each act at a point toward the right?
Ans. The resultant force is the sum of two forces.
Therefore F + F = 2F and direction is towards the right.
6. Define the conservation of linear momentum.
Ans. The sum of momenta of the two objects before the collision is equal to the sum of momenta after the collision, provided there is no external unbalanced the force acting on them. This is known as the law of conservation of momentum.
Or The total momentum is conserved during the interaction.
7. State the meaning of recoil of the gun.
Ans. When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun.
8. Give an example where two equal and opposite forces do not form an action-reaction pair.
Ans. When a body moves in a circular path, two forces act on it and they are the centripetal and centrifugal force which is equal and opposite. These are not action and reaction force because action and reaction always act on two different objects
9. State Newton's first law. Why is it known as the law of inertia?
Ans. According to Newton's first law of motion, if a body is in rest, it will remain in the state of rest, and if it is in a state of motion, it will remain moving in the same direction with uniform velocity unless an external force is applied on it.
It is known as the law of inertia because this property of an object by virtue of which it neither changes its present state nor it tends to change the present state, is called inertia.
10. Differentiate between mass and weight?
Ans. Differences between mass and weight are:
(i) Mass of a body is a measure of the quantity of matter contained in the body where weight is the force by which the earth attracts the body.
(ii) Mass is a scalar quantity, weight is a vector quantity.
(iii) It is constant for the body and does not change by changing the place of the body, weight is not constant but varies from place to place
11. What are the factors on which inertia depends?
Ans. The factor on which inertia depends directly, are mass and acceleration.
The greater the mass, the greater is the inertia of the body.
More the mass of a body more difficult it is to move the body from rest or to stop the body if it is initially moving.
Similarly the greater the acceleration, the greater is the inertia of the body.
12. State Newton's second law of motion.
Ans. The first law of motion indicates that when an unbalanced external force acts on an object, its velocity changes, that is the object gets an acceleration and the acceleration of an object depends on the force applied to it. Newton's second law of motion gives the quantitative value of force.
Therefore F = ma.
13. State Newton's second law in terms of momentum.
Ans. According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the force applied on it and the change in momentum is in the direction in which the force is applied.
14. Explain Newton's first law in terms of the second law.
Ans. The first law of motion can be mathematically stated from the mathematical expression for the second law of motion.
F = ma or F = m(v − u)/ t
or F= (mv – mu)/t .That is when F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest. This is the newtons second law.
15. A book kept on a table. There are two forces on the book -normal force in the upward direction and gravitational force in a downward direction. Is this pair of force is an action-reaction pair? Explain your answer.
Ans. No, because according to the third law of motion which states that when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These forces act on different objects and never on the same object and the book is the only object on which both forces act.
16. Define inertia. What are the two types of inertia?
Ans. All objects resist a change in their state of motion. In a qualitative way, the tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia.
There are two types of inertia: The motion of inertia and the rest of inertia.
17. If an object experiences a non zero external unbalanced force. Is it possible for the object to be traveling with a non zero velocity? State your answer.
Ans. Yes, Is it possible for the object to be traveling with a non zero velocity if the resistance between air and the moving object is zero and the object moving with uniform motion because the external unbalanced force is needed to initiate the motion.
18. karate player can break a pile of tiles in a single blow with his hands. How?
Ans. Karate player moves his hand with high speed due to which momentum force increases and strikes the pile with his hand very fast. Thus the entire momentum of the fast-moving hand is reduced to zero in a very short time, due to this, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for breaking the pile of tiles.
19. Raju is having three solid blocks of the same size and shape and made up of steel, wood, and plastic. Which one of these will have the highest inertia. Give a reason for your choice.
Ans. Solid blocks made up of steel will have the highest inertia, because steel has more mass and inertia depends on mass directly. Therefore greater the mass, the greater is the inertia of the object.
III. Long answer type questions:
Ans. (i) Force - Force is an external cause that can change the state of rest or the state of motion of an object. It is a vector quantity and the S.I unit is N.
(ii) Contact force - A force exerted on a body when it is in contact with the body is called contact force. Example - Push or pull, Muscular force, etc.
(iii) Non-contact force - A force exerted on a body without any contact with two bodies is called contact force. Example - Gravitational force. Electrostatic force etc.
(iii) Frictional force - Frictional force is the force caused by the relative motion of two surfaces that come in contact with each other.
2. When a wheel rolls on the level ground, What is the direction of frictional force at the point of contact of the wheel and ground? How is it in accordance with Newton's third law of motion?
Ans. When a wheel is rolling at a constant velocity, then the acceleration is zero, so the frictional force is zero. If the wheel is accelerating (speeding up or slowing down) then the frictional force is in the opposite direction of the acceleration.
Ans. When a wheel is rolling at a constant velocity, then the acceleration is zero, so the frictional force is zero. If the wheel is accelerating (speeding up or slowing down) then the frictional force is in the opposite direction of the acceleration.
Newton’s Third Law tells us that the frictional force exerted on the wheel by the ground is exactly equal but opposite to the force exerted by the wheel on the ground.
3. When a tree is shaken, its fruits and leaves fall down. Why?
Ans. It is due to the inertia of rest in which an object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
When a tree is shaken, it brings a motion in the tree but its fruits and leaves tend to continue in the same state of rest because of its inertia which causes the leaves and fruits to separate from its branch and fall down.
Ans. It is due to the inertia of rest in which an object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
When a tree is shaken, it brings a motion in the tree but its fruits and leaves tend to continue in the same state of rest because of its inertia which causes the leaves and fruits to separate from its branch and fall down.
4. Mention the action and reaction forces for a man walking on the road.
Ans. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. when we push the road below backward, the road exerts an equal and opposite reaction force on our feet to make we move forward.
Ans. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. when we push the road below backward, the road exerts an equal and opposite reaction force on our feet to make we move forward.
5. Action and reaction forces act on the same or different bodies? Explain and justify your answer.
Ans. Action and reaction forces act on different bodies. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object. These two opposing forces are also known as action and reaction forces.
Ans. Action and reaction forces act on different bodies. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. These forces act on different objects and never on the same object. These two opposing forces are also known as action and reaction forces.
6. Using the Second law of motion derive the relation between force and acceleration.
Ans. The mathematical formulation of the second law of motion:
If the mass of an object is m and moving along a straight line with an initial velocity u. It is uniformly accelerated to velocity v in time t by the application of a constant force F throughout the time t.
The initial and final momentum of the object will be
p1 = mu and p2 = mv respectively.
The change in momentum = p2 – p1 = mv – mu
= m × (v – u).
The rate of change of momentum = m (v - u )/ t
According to Newtons second law
The applied force F ∝ m (v−u ) /t
F= km (v- u)/ t
F = kma : Here [a (acceleration)= (v – u)/t ]
The quantity, k is a constant of proportionality. If the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
That is, 1 unit of force = k × (1 kg) × (1 m/s2).
Thus the value of k becomes 1.
From Eq. F = ma
The unit of force is kg m/s2 or Newton N.
Ans. The mathematical formulation of the second law of motion:
If the mass of an object is m and moving along a straight line with an initial velocity u. It is uniformly accelerated to velocity v in time t by the application of a constant force F throughout the time t.
The initial and final momentum of the object will be
p1 = mu and p2 = mv respectively.
The change in momentum = p2 – p1 = mv – mu
= m × (v – u).
The rate of change of momentum = m (v - u )/ t
According to Newtons second law
The applied force F ∝ m (v−u ) /t
F= km (v- u)/ t
F = kma : Here [a (acceleration)= (v – u)/t ]
The quantity, k is a constant of proportionality. If the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
That is, 1 unit of force = k × (1 kg) × (1 m/s2).
Thus the value of k becomes 1.
From Eq. F = ma
The unit of force is kg m/s2 or Newton N.
7. When a carpet is bitten with a stick it releases dust. Explain why?
Ans. It is due to the inertia of rest in which an object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
When a carpet is bitten with a stick, carpet comes in motion but its dust tends to continue in the same state of rest because of its inertia which causes the dust to separate from the carpet and fall down.
Ans. It is due to the inertia of rest in which an object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.
When a carpet is bitten with a stick, carpet comes in motion but its dust tends to continue in the same state of rest because of its inertia which causes the dust to separate from the carpet and fall down.
8. State an example, how force can change the velocity of a body? Write the type of force acting between moving body and floor.
Ans. According to the newtons 2nd law, F = ma, therefore, a force can cause acceleration on a moving body and acceleration means a change in velocity at constant rate i.e, a force can change the velocity of a body E.g., a moving ball comes to rest
The frictional force acting in the opposite direction of motion between moving body and floor.
9. (a) If action is always equal to the reaction, explain how a horse can pull a cart?
(b) Write the units of force and momentum.
Ans. (a) When a horse pushes the ground in the backward direction, the earth exerts a reaction force in the forward direction. The force exerted by the horse is action force and force exerted by the earth is reaction force. According to Newton's third law of motion action and reaction, forces are equal and opposite. With the help of the reaction force exerted by the earth, a horse can pull the cart.
(b) The unit of force is kg m/s2 or Newton N.
The unit of momentum is Kg m/s.
10. Interpret force in terms of momentum. Represent the following graphically. (i) Momentum versus velocity when mass is fixed (ii) Momentum versus mass when velocity is constant.
Ans. Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity. Momentum p = mv . Momentum has both direction and magnitude. Its direction is the same as that of velocity, v.
The SI unit of momentum is kilogram-meter per second (kg m/s).
Momentum is directly proportional to mass and velocity.
(i) As momentum is directly proportional to velocity so when mass is the constant graph of momentum versus velocity will be straight.
p (momentum) ∝ v (velocity)
(ii) As momentum is directly proportional to mass so when velocity is the constant graph of momentum versus mass will be straight.
p (momentum) ∝ v (velocity)
Ans. Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity. Momentum p = mv . Momentum has both direction and magnitude. Its direction is the same as that of velocity, v.
The SI unit of momentum is kilogram-meter per second (kg m/s).
Momentum is directly proportional to mass and velocity.
(i) As momentum is directly proportional to velocity so when mass is the constant graph of momentum versus velocity will be straight.
p (momentum) ∝ v (velocity)
(ii) As momentum is directly proportional to mass so when velocity is the constant graph of momentum versus mass will be straight.
p (momentum) ∝ v (velocity)
11. (a)To start walking we push the ground in the backward direction. Why?
(b) Why are the athletes in a high jump event made to fall on the sand or cushioned bed?
Ans. (a) According to Newton's third law of motion action and reaction, forces are equal and opposite. To start walking we push the ground in the backward direction to get equal and opposite reaction force in the forward direction to move forward.
(b) In a high jump athletic event, the athletes are made to fall either on a cushioned bed or on a sand bed. This is to increase the time of the athlete’s fall to stop after making the jump. This decreases the rate of change of momentum and hence the force.
(b) Why are the athletes in a high jump event made to fall on the sand or cushioned bed?
Ans. (a) According to Newton's third law of motion action and reaction, forces are equal and opposite. To start walking we push the ground in the backward direction to get equal and opposite reaction force in the forward direction to move forward.
(b) In a high jump athletic event, the athletes are made to fall either on a cushioned bed or on a sand bed. This is to increase the time of the athlete’s fall to stop after making the jump. This decreases the rate of change of momentum and hence the force.
12. If the table tennis ball hits player it does not hurt him but a fast moving ball may hurt him. Why?
Ans. If the table tennis ball hits player it does not hurt him but a fast moving ball may hurt him because the impact produced by the objects depends on their mass and velocity. If the velocity of the tennis ball is greater, the impact produced by the fast-moving ball also increases which can hurt.
Ans. If the table tennis ball hits player it does not hurt him but a fast moving ball may hurt him because the impact produced by the objects depends on their mass and velocity. If the velocity of the tennis ball is greater, the impact produced by the fast-moving ball also increases which can hurt.
13. Water sprinkled used for the grass lawn being to rotate as soon as the water is supplied. Explain the principle on which it works.
Ans. The principal is Newton's third law of motion in which one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. As the water comes out from the water sprinkler water exerts an equal and opposite backward reaction force to the sprinkler and it starts to rotate.
Ans. The principal is Newton's third law of motion in which one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. As the water comes out from the water sprinkler water exerts an equal and opposite backward reaction force to the sprinkler and it starts to rotate.
14. By applying force, if the object does not move then what type of force is acting on it?
Ans. By applying force, if the object does not move it means an equal and opposite reaction force is acting on it which is a frictional force. The action force applied on the object and reaction force exerted by the surface in the opposite direction both are balanced each other and due to this, the object does not move. It is based on Newton's third law of motion.
Ans. By applying force, if the object does not move it means an equal and opposite reaction force is acting on it which is a frictional force. The action force applied on the object and reaction force exerted by the surface in the opposite direction both are balanced each other and due to this, the object does not move. It is based on Newton's third law of motion.
15. State Newton’s third law of motion and how does it explain the walking of man on the ground.
Ans. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction.
If we are standing at rest and intend to start walking on a road. we must accelerate, and this requires a force in accordance with the second law of motion. We push the road below backward. The road exerts an equal and opposite reaction force on our feet to make us move forward.
Ans. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction.
If we are standing at rest and intend to start walking on a road. we must accelerate, and this requires a force in accordance with the second law of motion. We push the road below backward. The road exerts an equal and opposite reaction force on our feet to make us move forward.
16. When a bullet is fired from a gun, the gun recoils. Why?
Ans. When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun. Since the gun has a much greater mass than the bullet, the acceleration of the gun is much less than the acceleration of the bullet.
17. Two identical bullets are fired, one by a lighter rifle and another by a heavy rifle with the same force. Which rifle will hurt the shoulder more and why?
Ans. Bullets are identical means masses are same and fired with the same force so the momentum of both bullets is the same. According to the conservation of momentum, the rifle recoils with the same momentum as that of the bullet.
We know that momentum = mass x velocity;
So to conserve momentum light rifle will recoil with larger velocity as it has less mass and heavy rifle recoil with less velocity as it has more mass.
Therefore light rifle will hurt the shoulder more.
Ans. Bullets are identical means masses are same and fired with the same force so the momentum of both bullets is the same. According to the conservation of momentum, the rifle recoils with the same momentum as that of the bullet.
We know that momentum = mass x velocity;
So to conserve momentum light rifle will recoil with larger velocity as it has less mass and heavy rifle recoil with less velocity as it has more mass.
Therefore light rifle will hurt the shoulder more.
18. When a cricketer fielding near the boundary takes a high catch, he moves his hands downward with the ball. Why does he do that?
Ans. When a cricketer fielding near the boundary takes a high catch, he moves his hands downward with the ball, in doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is decreased and therefore the impact of catching the fast moving ball is also reduced. If the ball is stopped suddenly then its high velocity decreases to zero in a very short interval of time. Thus, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.
Ans. When a cricketer fielding near the boundary takes a high catch, he moves his hands downward with the ball, in doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is decreased and therefore the impact of catching the fast moving ball is also reduced. If the ball is stopped suddenly then its high velocity decreases to zero in a very short interval of time. Thus, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.
19. Explain why is it difficult for a fireman to hold a hose which ejects a large amount of water at a high velocity.
Ans. When a hose ejects a large amount of water at a high velocity, its momentum is high and according to Newton's Third Law of Motion, water pushes the hose in the backward direction with the same and large force. Therefore, it is difficult for a fireman to hold a hose which ejects a large amount of water at a high velocity.
Ans. When a hose ejects a large amount of water at a high velocity, its momentum is high and according to Newton's Third Law of Motion, water pushes the hose in the backward direction with the same and large force. Therefore, it is difficult for a fireman to hold a hose which ejects a large amount of water at a high velocity.
20. (a) A horse is continuous to apply a force in order to move a cart with a constant velocity. Explain why?
(b) A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?
Ans. (a) When a horse moves a cart, a frictional force between the wheel of cart and road starts working in the opposite to the motion, which slows down the motion of the cart, so horse needs to apply continuously force in forwarding direction to maintain a constant velocity.
(b) A truck of mass M is moved under a force F.
Its acceleration (a) = F/M
When the truck is loaded with an object equal to the mass of the truck and the driving force is halved, then its total mass will be 2M and force becomes F/2.
New acceleration (a') = F/2 = F/4M = 1/4 (F/M) = 1/4th a.
2M
Now the acceleration changes to one fourth.
(b) A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?
Ans. (a) When a horse moves a cart, a frictional force between the wheel of cart and road starts working in the opposite to the motion, which slows down the motion of the cart, so horse needs to apply continuously force in forwarding direction to maintain a constant velocity.
(b) A truck of mass M is moved under a force F.
Its acceleration (a) = F/M
When the truck is loaded with an object equal to the mass of the truck and the driving force is halved, then its total mass will be 2M and force becomes F/2.
New acceleration (a') = F/2 = F/4M = 1/4 (F/M) = 1/4th a.
2M
Now the acceleration changes to one fourth.
21. Prove the principle of conservation of linear momentum for two bodies moving in the same direction and coiling.
Ans. Suppose two objects balls A and B of masses mA and mB are traveling in the same direction along a straight line at different velocities uA and uB, respectively. And there are no other external unbalanced forces acting on them.
Let uA > uB and the two balls collide with each other. During collision which lasts for a time t, the ball A exerts a force FAB on ball B and the ball B exerts a force FBA on ball A.
Suppose vA and vB are the velocities of the two balls A and B after the collision, respectively. The momentum of ball A before the collision is mAuA and the momentum after the collision is mAvA,.
The rate of change of its momentum during the collision will be
= (mA vA- mAuA) /t
= mA( vA - uA) / t
Similarly, the rate of change of momentum of ball B (= FBA or reaction) during the collision will be
= mB ( vB - uB) / t .
According to the third law of motion, the force FAB exerted by ball A on ball B (action)and the force FAB exerted by the ball B on ball A (reaction) must be equal and opposite to each other.
Therefore, FAB = – FBA or
mA( vA - uA) / t = mB ( vB - uB) / t
or mAvA - mAuA = mBvB - mBuB
or mAuA+ mBuB = mAvA + mBvA
This proves the total momentum of the two balls remains unchanged or conserved provided no other external force acts.
Ans. Suppose two objects balls A and B of masses mA and mB are traveling in the same direction along a straight line at different velocities uA and uB, respectively. And there are no other external unbalanced forces acting on them.
Let uA > uB and the two balls collide with each other. During collision which lasts for a time t, the ball A exerts a force FAB on ball B and the ball B exerts a force FBA on ball A.
Suppose vA and vB are the velocities of the two balls A and B after the collision, respectively. The momentum of ball A before the collision is mAuA and the momentum after the collision is mAvA,.
The rate of change of its momentum during the collision will be
= (mA vA- mAuA) /t
= mA( vA - uA) / t
Similarly, the rate of change of momentum of ball B (= FBA or reaction) during the collision will be
= mB ( vB - uB) / t .
According to the third law of motion, the force FAB exerted by ball A on ball B (action)and the force FAB exerted by the ball B on ball A (reaction) must be equal and opposite to each other.
Therefore, FAB = – FBA or
mA( vA - uA) / t = mB ( vB - uB) / t
or mAvA - mAuA = mBvB - mBuB
or mAuA+ mBuB = mAvA + mBvA
This proves the total momentum of the two balls remains unchanged or conserved provided no other external force acts.
22. A ball of mass m is thrown vertically upward with an initial velocity V. Its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed V again before striking the ground. It implies that the magnitude of the initial and final momentum of the ball is the same. Yet it is not an example of conservation of momentum. Explain why?
Ans. According to the conservation of linear momentum, the momentum is conserved if no external forces act on the system. The ball is under the influence of an external force called gravitational force. Hence the momentum is not conserved.
If the upward direction is taken as positive, the initial momentum of the ball is MU and the final momentum is MV. Though the magnitude is the same, the direction is different. Hence we cannot apply conservation of momentum.
23. Write the factors on which solid and liquid pressure depends.
Ans. Factors of solid pressure: The pressure exerted on a surface depends on
(i) Force or thrust and - Larger the force on the surface, larger is the pressure exerted on it
(ii) Area on which thrust is applied- Larger the area, less is the pressure exerted on it.
Factors of liquid pressure : The pressure at a point inside the liquid depends on
(i) depth of the point below the surface- Larger the depth of the point, larger is the pressure exerted on it
(ii) density of the liquid- Larger the density of the liquid, larger is the pressure exerted on it
(iii) acceleration due to gravity- Larger the acceleration due to gravity larger is the pressure exerted on it.
1. What is the momentum of a body of mass 200g moving with a velocity of 15 m/s?
Ans. Momentum = mv
m = 200g = 200/1000 = 0.2 kg.
v = 15 m/s.
mv = 0.2 x 15 = 3 kgm/s.
2. A cheetah accelerates from rest at the rate of 4 m/s^2.
(a) What will be the velocity attained by it in 10 s?
(b) How far will it travel in this duration?
Ans. According to the conservation of linear momentum, the momentum is conserved if no external forces act on the system. The ball is under the influence of an external force called gravitational force. Hence the momentum is not conserved.
If the upward direction is taken as positive, the initial momentum of the ball is MU and the final momentum is MV. Though the magnitude is the same, the direction is different. Hence we cannot apply conservation of momentum.
23. Write the factors on which solid and liquid pressure depends.
Ans. Factors of solid pressure: The pressure exerted on a surface depends on
(i) Force or thrust and - Larger the force on the surface, larger is the pressure exerted on it
(ii) Area on which thrust is applied- Larger the area, less is the pressure exerted on it.
Factors of liquid pressure : The pressure at a point inside the liquid depends on
(i) depth of the point below the surface- Larger the depth of the point, larger is the pressure exerted on it
(ii) density of the liquid- Larger the density of the liquid, larger is the pressure exerted on it
(iii) acceleration due to gravity- Larger the acceleration due to gravity larger is the pressure exerted on it.
Numerical:
1. What is the momentum of a body of mass 200g moving with a velocity of 15 m/s?
Ans. Momentum = mv
m = 200g = 200/1000 = 0.2 kg.
v = 15 m/s.
mv = 0.2 x 15 = 3 kgm/s.
2. A cheetah accelerates from rest at the rate of 4 m/s^2.
(a) What will be the velocity attained by it in 10 s?
(b) How far will it travel in this duration?
Ans. Acceleration of cheetah = 4 m/s^2, initial velocity = 0 m/s, and
time = 10s.
(a) The velocity attained by cheetah v = u + at.
v = 0 + 4 x 10 = 40 m/s.
(b) Distance covered by cheetah = speed x time = 40 x 10 = 400 m.
3. A force of 25 N acts on a mass of 500 g resting on a frictionless surface. What is the acceleration produced?
Ans. Force F = ma
mass m = 500g= 0.5 kg and Force F = 25N.
Acceleration a = F/m = 25 / 0.5 = 250/5 = 50 m/s^2.
4. A force of 15 N acts for 5 s on a body of mass 5 kg which is initially at rest. Calculate :
(a) the final velocity of the body b) the displacement of the body.
Ans. Given : Force F = 15 N, mass m = 5kg and time t = 5 s and initial velocity u = 0 m/s.
F = ma = 5 x a
a = F / m = 15 / 5 = 3 m/s^2
(a) The final velocity v = u + at = 0 + 3x5 = 15 m/s.
(b) The displacement of the body S = ut + 1/2at^2
S = 0 x 5 + 1/2 x 3 x 25.
S = 75/2 = 37.5 m.
5. A scooter is moving with a velocity of 20 m/s when brakes are applied. The mass of the scooter and the rider is 180 Kg. the constant force applied by the brakes is 500 N.
(a) How long should the brakes be applied to make the scooter comes to a halt?
(b) How far does the scooter travel before it comes to rest?
(a) How long should the brakes be applied to make the scooter comes to a halt?
(b) How far does the scooter travel before it comes to rest?
Ans. Force F = 500N. mass m = 180 kg. final velocity v = 0 m/s, and initial velocity u = 20 m/s.
(a) We know that F = ma
a = F/m
a = 500/180 = 50/18 = 25/9 m/s^2
The time should the brakes be applied to make the scooter comes to a halt
t = (v - u) /a
t = (0 - 20)x9 /25
t = 36/5 = 7.2s
(b) Distance S = ut + 1/2 at^2
S = 1 x 25 x 36 x 36 = 4 x 18 = 72 m.
2 x 9 x 5 x 5
6. A stone is dropped from a 100 m high tower. How long does it take to fall?
(i) the first 50 m and (ii) the second 50 m.
(i) the first 50 m and (ii) the second 50 m.
Ans. We have h = ut + 1/2gt^2 here u = 0 m/s, and h = 100m.
100 = 1/2 x 10 x t^2
t^2 = 100 x 2 = 20 s
10
total time is taken = 4.47 s
(i) h = ut + 1/2 gt^2
50 = 1/2 x 10 x t^2
t^2 = 100/10 = 10s
t = 3.16 s.
The time is taken to fall in the first 50 m = 3.16 s
(ii) The time is taken to fall in the second 50 m = 4.47s - 3.16s = 1.13s
7. From a rifle of mass 4 kg, A bullet of mass 50 gram is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle.
Ans. Mass of refile = 4 kg, mass of bullet = 50 gm = 0.05 kg and initial velocity of bullet = 35 m/s.
According to the conservation of linear momentum:
MV = - mv
(where M = mass of refile, V = recoilo velocity of refile, m = mass of bullet and v = velocity of bullet)
MV = - mv
V = - mv/M = (- 0.05 x 35)/4 = 1.75/4 = 0.438 = 0.44 m/s
8. Two objects of mass 100 g and 200 g are moving along the same direction with a velocity of 2m p/s and 1 m p/s respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. Determine the velocity of the second object.
Ans. Let there are two objects A and B. Before collision mass of A M = 100g, velocity V1 = 2m/s, mass of second object m = 200g, and velocity v1 = 1m/s
After the collision velocity of A becomes V2 = 1.67m/s and velocity of B = v2.
According to the conservation of linear momentum:
MV1 + mv1 = - (MV2 + mv2)
100 x 2 + 200 x 1 = 100 x 1.67 + 200 x v2
200 + 200 = 167 + 200v2
v2 = (400 - 167)/200
v2 = 233/200
v2 = 1.165m/s
9. Two friends on roller skates are standing 5 m apart facing each other. One of them throws a ball of 2 kg towards the other, who catches it. How will this activity affect the position of the two? Explain.
Ans. The distance between them will increase. The momentum of both of them is zero as they are at rest initially. According to the conservation of the momentum, the one who throws the ball would move backward. The second will experience a net force after catching the ball and therefore will move backward that is in the direction of the force.
10. A bullet of mass 10 g strikes a sandbag at a speed of 103 m/s and gets embedded after traveling 5 cm. Calculate
(i) the resistive force exerted by the sand on the bullet
(ii) the time is taken by the bullet to come to rest.
Ans. Mass of bullet =10gm=0.01kg
Initial velocity (U)of bullet=1000m/s
Final velocity (V)=0m/s
Displacement of bullet=5cm=0.05m
a) We have 2as=V2 -U2
2 x a x 0.05 =02-10002
2 x a x 5/100 =-1000000
2a x 1/20 =-1000000
a x 1/10 =-1000000
a=-10000000=-107
Now we have F=ma
F=0.01(10000000)
F=1/100(10000000)
F=-100000N
Therefore the resistive force of bullet =-100000N.
b) We know that a=(v-u) / t
-10000000 = 0-1000 / t
-10000000 = -1000/t
-10000=t
t = -10⁴s.
10. Derive the unit of force using the second law of motion a force of 5N produce an acceleration of 8 m/s2on a mass M1 and an acceleration of 24 m/s2 on a mass M2. What acceleration of the same force provide if both the masses are tied together.
Ans. According to the second law of motion:
F = ma
mass of M1 = F/a = 5/8 g.
and mass M2 = F/a = 5/24 g.
When both the masses are tied together, total mass = 5/8 + 5/24 = 20/24 g.
The acceleration of the same force provides if both the masses are tied together = F/m = 5 x 24/20 = 120/20 =6 m/s2
11. A force produces an acceleration of 0.5 m/s2 in a body of mass 3.0 Kg. If the same force acts on a body of mass 1.5 kg, what will be its acceleration?
Ans. In the first case acceleration (a) = 0.5 m/s2
and mass (m) = 3 kg.
F = ma = 3 x 0.5 = 1.5 N.
In the second case, if the same force acts on a body then
F = ma
1.5 = 1.5 x a
acceleration of 2nd body (a) = 1.5/1.5 = 1m/s2
12. A force produces an acceleration of 5.0 m/s2 when it acts on a body of mass 20 grams. Find the force in Newtons.
Ans. According to the second law of motion, F = ma
F = 20 x 5 = 100 N.
13. A force acts on a particle of mass 200 gm. The velocity of the particle changes from 15 m/s to 25 m/s in 2.5 s. Assuming the force to be constant, find its magnitude.
Ans. Given u = 15 m/s and v = 25 m/s, mass = 200g=0.2 kg and time t = 2.5 s.
We have v = u + at
a = (v - u)/t
a = (25 - 15)/2.5
a = 10/2.5 = 100/25 = 4 m/s2
Therefor F = ma = 0.2 x 4 =0.8 N
14. A force produces an acceleration of 2.0 m/s2 in a body a and 5.0 m/s2 in another body B. Find the ratio of the mass of A to the mass of B.
Ans. Let the mass of the first body be = m1 and acceleration be = 2.0 m/s2
mass of the second body be = m2 and acceleration be = 5.0 m/s2
The ratio mass A to the mass of B = m1/m2 = ( F x a2)/(a1 x F) = a2/a1
a2/a1 = 5/2
Ans. 5:2
15. A force of 0.6 N on a particle increases its velocity from 5.0 m/s to 6.0 m/s in 2 sec. Find the mass of the particle.
Ans. Given F = 0.6N, u = 5.0 m/s and v = 6.0 m/s
a = (v - u)/t = (6 - 5)/2 = 1/2 m/s2F = ma
m = F / a = 0.6 x 2 = 1.2 kg
16. A force acting on a particle of mass 200 gm displaces it through 400 cm in 2 sec. Find the magnitude of the force if the initial velocity of the particle is zero.
Ans. Given u = 0 m/s, mass m = 200 g = 0.2 kg, displacement s = 400 cm
= 4m and time t = 2 s.
We have S = ut + 1/2 at2
S = 1/2 at2
a = 2S/t2
a = 2 x 4 / 2 x 2 = 8/4 = 2 m/s2
According to the second law, F = ma = 0.2 x 2 = 0.4N
17. A bullet of mass 20 gm moving with a speed of 120 m/s strikes a thick muddy wall and penetrate into it. It takes 0.03 seconds to stop in the wall. Find:
(a) the acceleration of the bullet in the wall,
(b) the force exerted by the wall on the bullet,
(c) the force exerted by the bullet on the wall, and
(d) the distance covered by the bullet in the wall.
Ans. Given mass m = 20 g = 0.02 kg, initial velocity u = 120m/s,
Time t to stop in the wall = 0.03s and final velocity v = 0 m/s.
We have v = u + at
a = v - u/t
( a) a = - 120/0.03 = - 4000 m/s2
(b) F = ma = 0.02 x 4000 = 80 N
(c) -80N
(d) Distance s = speed x time
s = 120 x 0.03 = 3.6m
18. A particle of mass 0.5 kg is kept at rest. A force of 2.0 N act on it for 5.0 sec. Find the distance moved by the particles in this 5.0 sec, and be the next 5.0 s.
Ans. We have F = ma
a = F/m
a = 2/0.5=4m/s²
Distance covered in first 5 sec
s = ut +1/2at²
s = 1/2 x 4 x 5²
s = 50m
The distance covered in the first 10 sec
s = 1/2 x 4 x 10²
s = 200m.
The distance covered in next 5 sec is 200-50 = 150m
Ans. Mass of refile = 4 kg, mass of bullet = 50 gm = 0.05 kg and initial velocity of bullet = 35 m/s.
According to the conservation of linear momentum:
MV = - mv
(where M = mass of refile, V = recoilo velocity of refile, m = mass of bullet and v = velocity of bullet)
MV = - mv
V = - mv/M = (- 0.05 x 35)/4 = 1.75/4 = 0.438 = 0.44 m/s
8. Two objects of mass 100 g and 200 g are moving along the same direction with a velocity of 2m p/s and 1 m p/s respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. Determine the velocity of the second object.
Ans. Let there are two objects A and B. Before collision mass of A M = 100g, velocity V1 = 2m/s, mass of second object m = 200g, and velocity v1 = 1m/s
After the collision velocity of A becomes V2 = 1.67m/s and velocity of B = v2.
According to the conservation of linear momentum:
MV1 + mv1 = - (MV2 + mv2)
100 x 2 + 200 x 1 = 100 x 1.67 + 200 x v2
200 + 200 = 167 + 200v2
v2 = (400 - 167)/200
v2 = 233/200
v2 = 1.165m/s
9. Two friends on roller skates are standing 5 m apart facing each other. One of them throws a ball of 2 kg towards the other, who catches it. How will this activity affect the position of the two? Explain.
Ans. The distance between them will increase. The momentum of both of them is zero as they are at rest initially. According to the conservation of the momentum, the one who throws the ball would move backward. The second will experience a net force after catching the ball and therefore will move backward that is in the direction of the force.
10. A bullet of mass 10 g strikes a sandbag at a speed of 103 m/s and gets embedded after traveling 5 cm. Calculate
(i) the resistive force exerted by the sand on the bullet
(ii) the time is taken by the bullet to come to rest.
Ans. Mass of bullet =10gm=0.01kg
Initial velocity (U)of bullet=1000m/s
Final velocity (V)=0m/s
Displacement of bullet=5cm=0.05m
a) We have 2as=V2 -U2
2 x a x 0.05 =02-10002
2 x a x 5/100 =-1000000
2a x 1/20 =-1000000
a x 1/10 =-1000000
a=-10000000=-107
Now we have F=ma
F=0.01(10000000)
F=1/100(10000000)
F=-100000N
Therefore the resistive force of bullet =-100000N.
b) We know that a=(v-u) / t
-10000000 = 0-1000 / t
-10000000 = -1000/t
-10000=t
t = -10⁴s.
10. Derive the unit of force using the second law of motion a force of 5N produce an acceleration of 8 m/s2on a mass M1 and an acceleration of 24 m/s2 on a mass M2. What acceleration of the same force provide if both the masses are tied together.
Ans. According to the second law of motion:
F = ma
mass of M1 = F/a = 5/8 g.
and mass M2 = F/a = 5/24 g.
When both the masses are tied together, total mass = 5/8 + 5/24 = 20/24 g.
The acceleration of the same force provides if both the masses are tied together = F/m = 5 x 24/20 = 120/20 =6 m/s2
11. A force produces an acceleration of 0.5 m/s2 in a body of mass 3.0 Kg. If the same force acts on a body of mass 1.5 kg, what will be its acceleration?
Ans. In the first case acceleration (a) = 0.5 m/s2
and mass (m) = 3 kg.
F = ma = 3 x 0.5 = 1.5 N.
In the second case, if the same force acts on a body then
F = ma
1.5 = 1.5 x a
acceleration of 2nd body (a) = 1.5/1.5 = 1m/s2
12. A force produces an acceleration of 5.0 m/s2 when it acts on a body of mass 20 grams. Find the force in Newtons.
Ans. According to the second law of motion, F = ma
F = 20 x 5 = 100 N.
13. A force acts on a particle of mass 200 gm. The velocity of the particle changes from 15 m/s to 25 m/s in 2.5 s. Assuming the force to be constant, find its magnitude.
Ans. Given u = 15 m/s and v = 25 m/s, mass = 200g=0.2 kg and time t = 2.5 s.
We have v = u + at
a = (v - u)/t
a = (25 - 15)/2.5
a = 10/2.5 = 100/25 = 4 m/s2
Therefor F = ma = 0.2 x 4 =0.8 N
14. A force produces an acceleration of 2.0 m/s2 in a body a and 5.0 m/s2 in another body B. Find the ratio of the mass of A to the mass of B.
Ans. Let the mass of the first body be = m1 and acceleration be = 2.0 m/s2
mass of the second body be = m2 and acceleration be = 5.0 m/s2
The ratio mass A to the mass of B = m1/m2 = ( F x a2)/(a1 x F) = a2/a1
a2/a1 = 5/2
Ans. 5:2
15. A force of 0.6 N on a particle increases its velocity from 5.0 m/s to 6.0 m/s in 2 sec. Find the mass of the particle.
Ans. Given F = 0.6N, u = 5.0 m/s and v = 6.0 m/s
a = (v - u)/t = (6 - 5)/2 = 1/2 m/s2F = ma
m = F / a = 0.6 x 2 = 1.2 kg
16. A force acting on a particle of mass 200 gm displaces it through 400 cm in 2 sec. Find the magnitude of the force if the initial velocity of the particle is zero.
Ans. Given u = 0 m/s, mass m = 200 g = 0.2 kg, displacement s = 400 cm
= 4m and time t = 2 s.
We have S = ut + 1/2 at2
S = 1/2 at2
a = 2S/t2
a = 2 x 4 / 2 x 2 = 8/4 = 2 m/s2
According to the second law, F = ma = 0.2 x 2 = 0.4N
17. A bullet of mass 20 gm moving with a speed of 120 m/s strikes a thick muddy wall and penetrate into it. It takes 0.03 seconds to stop in the wall. Find:
(a) the acceleration of the bullet in the wall,
(b) the force exerted by the wall on the bullet,
(c) the force exerted by the bullet on the wall, and
(d) the distance covered by the bullet in the wall.
Ans. Given mass m = 20 g = 0.02 kg, initial velocity u = 120m/s,
Time t to stop in the wall = 0.03s and final velocity v = 0 m/s.
We have v = u + at
a = v - u/t
( a) a = - 120/0.03 = - 4000 m/s2
(b) F = ma = 0.02 x 4000 = 80 N
(c) -80N
(d) Distance s = speed x time
s = 120 x 0.03 = 3.6m
18. A particle of mass 0.5 kg is kept at rest. A force of 2.0 N act on it for 5.0 sec. Find the distance moved by the particles in this 5.0 sec, and be the next 5.0 s.
Ans. We have F = ma
a = F/m
a = 2/0.5=4m/s²
Distance covered in first 5 sec
s = ut +1/2at²
s = 1/2 x 4 x 5²
s = 50m
The distance covered in the first 10 sec
s = 1/2 x 4 x 10²
s = 200m.
The distance covered in next 5 sec is 200-50 = 150m
