CLASS 9 GRAVITATION

 

Worksheet 1

Class 8 - Science

Chapter: Gravitation

Maximum Marks: 30

Time: 1 Hour

Section A (1 Mark Each)

1. Define gravitation.
2. Who discovered the universal law of gravitation?
3. Write the SI unit of gravitational force.
4. What is the value of acceleration due to gravity (g) on Earth?
5. What happens to the weight of an object when taken to the Moon?

Section B (2 Marks Each)

6. State the universal law of gravitation and write its mathematical formula.
7. Differentiate between mass and weight.
8. Why does an object fall to the ground when dropped from a height?
9. How does the force of gravitation depend on the masses of objects?
10. Why do astronauts feel weightless in space?

Section C (3 Marks Each)

11. Calculate the gravitational force between two objects of masses 10 kg and 20 kg kept 2 m apart. (G = 6.674 × 10⁻¹¹ Nm²/kg²)
12. Explain why the weight of an object is different on Earth and the Moon.
13. A ball and a feather are dropped from the same height in a vacuum. Which one will reach the ground first and why?

Section D (4 Marks Each)

14. Derive the formula for acceleration due to gravity (g = GM/R²).
15. Explain how artificial satellites stay in orbit around the Earth.

Answers

Section A (1 Mark Each)

1. Define gravitation.

   • Gravitation is the force of attraction between any two objects in the universe.

2. Who discovered the universal law of gravitation?

   • Sir Isaac Newton discovered the universal law of gravitation.

3. Write the SI unit of gravitational force.

   • The SI unit of gravitational force is Newton (N).

4. What is the value of acceleration due to gravity (g) on Earth?

   • The value of g on Earth is 9.8 m/s².

5. What happens to the weight of an object when taken to the Moon?

   • The weight of an object decreases to 1/6th of its weight on Earth.

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Section B (2 Marks Each)

6. State the universal law of gravitation and write its mathematical formula.

   • Newton’s law of universal gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
   • Formula: $$F = \frac{G \cdot m_1 \cdot m_2}{r^2}$$F is the gravitational force, G is the universal gravitational constant, m₁ & m₂ are the masses of objects, and r is the distance between them.

7. Differentiate between mass and weight.

   Mass	Weight
   The amount of matter in an object.	The force exerted by gravity on an object.
   SI unit: Kilogram (kg).	SI unit: Newton (N).
   Remains constant everywhere.	Changes with gravity.

8. Why does an object fall to the ground when dropped from a height?

   • An object falls to the ground because of the gravitational force exerted by the Earth.

9. How does the force of gravitation depend on the masses of objects?

   • The force of gravitation is directly proportional to the product of the masses of the two objects. If mass increases, gravitational force increases.

10. Why do astronauts feel weightless in space?

• Astronauts feel weightless in space because they are in free fall along with their spacecraft due to the absence of a normal reaction force.

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Section C (3 Marks Each)

11. Calculate the gravitational force between two objects of masses 10 kg and 20 kg kept 2 m apart. (G = 6.674 × 10⁻¹¹ Nm²/kg²)

Using the formula:

$$F = \frac{G \cdot m_1 \cdot m_2}{r^2}$$ $$F = \frac{(6.674 × 10^{-11}) × (10) × (20)}{(2)^2}$$ $$F = \frac{(6.674 × 10^{-11}) × 200}{4}$$ $$F = \frac{1.3348 × 10^{-8}}{4}$$ $$F = 3.337 × 10^{-9} N$$

Final Answer: 3.337 × 10⁻⁹ N

12. Explain why the weight of an object is different on Earth and the Moon.

• The weight of an object depends on gravity. Since the Moon has only 1/6th the gravity of Earth, the weight of an object on the Moon is 1/6th of its weight on Earth.

13. A ball and a feather are dropped from the same height in a vacuum. Which one will reach the ground first and why?

• In a vacuum, both the ball and the feather will fall at the same rate and reach the ground together because there is no air resistance, and both experience the same acceleration due to gravity.

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Section D (4 Marks Each)

14. Derive the formula for acceleration due to gravity (g = GM/R²).

• Newton’s law of gravitation: $$F = \frac{G \cdot M \cdot m}{R^2}$$
• Newton’s second law of motion: $$F = m \cdot a$$
  
• Since acceleration due to gravity is g, we replace a with g: $$m \cdot g = \frac{G \cdot M \cdot m}{R^2}$$
• Cancelling m from both sides: $$g = \frac{G \cdot M}{R^2}$$
• This is the formula for acceleration due to gravity.

15. Explain how artificial satellites stay in orbit around the Earth.

• Artificial satellites remain in orbit because of the balance between gravitational force and their forward velocity.
• The satellite moves in a curved path due to gravity, but its tangential velocity prevents it from falling directly to Earth.
• This balance keeps the satellite in continuous motion around Earth.

Worksheet 2

Class 8 - Science

Chapter: Gravitation

Maximum Marks: 30

Time: 1 Hour

Section A (1 Mark Each)

1. What is the difference between gravity and gravitation?
2. What is the value of the universal gravitational constant (G)?
3. If the mass of an object is 5 kg, what will be its weight on Earth? (g = 9.8 m/s²)
4. Give one example of the effect of gravity in daily life.
5. Why does the Moon not fall into the Earth?

Section B (2 Marks Each)

6. What will happen if the value of G becomes zero?
7. Explain why the weight of an astronaut in a spacecraft is nearly zero.
8. How does gravitational force change when the distance between two objects is doubled?
9. Why do objects of different masses fall at the same rate in a vacuum?
10. Why is the value of acceleration due to gravity different on different planets?

Section C (3 Marks Each)

11. Calculate the weight of a 50 kg person on the Moon if the acceleration due to gravity on the Moon is 1.63 m/s².
12. Explain how tides are formed due to the gravitational pull of the Moon and the Sun.
13. A stone is thrown upwards. Explain how gravity affects its motion.

Section D (4 Marks Each)

14. Derive the relation between mass, weight, and acceleration due to gravity.
15. Why does the Earth attract the Moon, but the Moon does not crash into the Earth? Explain using Newton’s laws.

Answers

Section A (1 Mark Each)

1. What is the difference between gravity and gravitation?

   • Gravity is the force of attraction exerted by Earth on objects.
   • Gravitation is the general force of attraction between any two objects in the universe.

2. What is the value of the universal gravitational constant (G)?

   • The value of G is 6.674 × 10⁻¹¹ Nm²/kg².

3. If the mass of an object is 5 kg, what will be its weight on Earth? (g = 9.8 m/s²)

   • Weight (W) = mass × gravity $$W = 5 × 9.8 = 49 N$$
     
   • Answer: 49 Newtons (N).

4. Give one example of the effect of gravity in daily life.

   • Fruits falling from a tree due to the Earth’s gravity.

5. Why does the Moon not fall into the Earth?

   • The Moon stays in orbit because of its tangential velocity, which balances Earth’s gravitational pull, preventing it from falling.

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Section B (2 Marks Each)

6. What will happen if the value of G becomes zero?

   • If G = 0, there will be no gravitational force, objects will not be attracted to Earth, and planets will not orbit the Sun.

7. Explain why the weight of an astronaut in a spacecraft is nearly zero.

   • The astronaut experiences free fall along with the spacecraft, creating the sensation of weightlessness.

8. How does gravitational force change when the distance between two objects is doubled?

   • According to the formula: $$F = \frac{G \cdot m_1 \cdot m_2}{r^2}$$
   • If distance (r) is doubled, the gravitational force becomes 1/4th of the original force.

9. Why do objects of different masses fall at the same rate in a vacuum?

   • In a vacuum, there is no air resistance, and acceleration due to gravity (g = 9.8 m/s²) acts equally on all objects, causing them to fall at the same rate.

10. Why is the value of acceleration due to gravity different on different planets?

• g = GM/R², so the value of gravity depends on the planet’s mass (M) and radius (R). Since different planets have different masses and sizes, their gravitational pull varies.

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Section C (3 Marks Each)

11. Calculate the weight of a 50 kg person on the Moon if the acceleration due to gravity on the Moon is 1.63 m/s².

• Weight (W) = mass × gravity $$W = 50 × 1.63 = 81.5 N$$
• Answer: 81.5 N

12. Explain how tides are formed due to the gravitational pull of the Moon and the Sun.

• The Moon’s gravity pulls on Earth’s water, causing high tides in areas facing the Moon.
• The Sun’s gravity also affects tides, making them higher during full moon and new moon phases (spring tides).

13. A stone is thrown upwards. Explain how gravity affects its motion.

• As the stone moves up, gravity opposes the motion, slowing it down.
• At the highest point, velocity becomes zero, and then gravity pulls it back down.

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Section D (4 Marks Each)

14. Derive the relation between mass, weight, and acceleration due to gravity.

• Newton’s second law states: $$F = m \cdot a$$
  
• For weight, acceleration is due to gravity (g), so: $$W = m \cdot g$$
  
• Where W is weight (in Newtons), m is mass (in kg), and g is acceleration due to gravity (9.8 m/s² on Earth).
• Mass is constant, but weight changes depending on g.

15. Why does the Earth attract the Moon, but the Moon does not crash into the Earth? Explain using Newton’s laws.

• Newton’s Law of Universal Gravitation states that the Earth attracts the Moon due to its gravity.
• The Moon has tangential velocity, which prevents it from falling into Earth.
• This creates a stable orbit, balancing the Moon’s motion and Earth’s gravity.