Physics Question Bank – Gravitation

Question Bank – Gravitation

1. Very Short Answer Questions (1 Mark)

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

   • Answer: $6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$

2. State Newton’s law of gravitation.

   • Answer: Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

3. What is the gravitational force between two objects if the distance between them becomes half?

   • Answer: The force becomes four times the original force.

4. Define gravitational field.

   • Answer: The region around a mass in which another mass experiences a gravitational force is called a gravitational field.

5. At what height above the Earth's surface does the value of acceleration due to gravity become half?

   • Answer: At a height equal to the radius of the Earth.

6. What is the escape velocity on Earth?

   • Answer: $11.2 \, \text{km/s}$.

7. State Kepler’s first law.

   • Answer: Planets move in elliptical orbits with the Sun at one of the foci.

8. What is the shape of the orbit of a satellite around Earth?

   • Answer: Elliptical.

9. Why is ‘G’ called a universal constant?

   • Answer: Because its value remains the same throughout the universe.

10. What happens to the gravitational force when the mass of one of the objects is doubled?

• Answer: The force also doubles.

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2. Short Answer Questions (2 Marks)

11. How does the value of ‘g’ change with depth?

    • Answer: As depth increases, the value of 'g' decreases and becomes zero at the center of the Earth.

12. Write the relation between g and G.

    • Answer: $g = \frac{GM}{R^2}$, where G is the gravitational constant, M is the mass of Earth, and R is the radius of Earth.

13. Explain why astronauts in space feel weightlessness.

    • Answer: In space, the gravitational force from the Earth is balanced by the centrifugal force due to orbital motion, resulting in weightlessness.

14. What is the significance of escape velocity?

    • Answer: It is the minimum velocity required for an object to overcome the gravitational pull of the Earth.

15. Define orbital velocity.

    • Answer: Orbital velocity is the velocity with which a satellite needs to move to stay in a stable orbit around a planet.

16. How is gravitational potential energy at a height h related to mass m?

    • Answer: $U = mgh$, where g is the acceleration due to gravity.

17. What is the value of gravitational potential energy at infinity?

    • Answer: Zero.

18. Why does the Moon not fall towards the Earth?

    • Answer: The Moon is in a continuous state of free fall towards Earth, but its tangential velocity keeps it in orbit.

19. Why does the value of ‘g’ decrease with altitude?

    • Answer: As altitude increases, the distance from the Earth's center increases, reducing the value of g.

20. What is the direction of gravitational force?

    • Answer: Gravitational force is always attractive and directed towards the center of the mass.

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3. Numerical Problems (3 Marks)

21. Calculate the force of attraction between two 10 kg masses kept 1 meter apart.

    • Answer:
      $F = G \frac{m_1 m_2}{r^2}$
      $F = 6.674 \times 10^{-11} \times \frac{10 \times 10}{1^2}$
      $F = 6.674 \times 10^{-9} \, \text{N}$

22. A satellite is orbiting Earth at an altitude equal to the Earth's radius. Calculate the orbital speed.

    • Answer:
      $v = \sqrt{\frac{GM}{2R}}$
      Using $G = 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$ and $R = 6.37 \times 10^6 \, \text{m}$.

23. What is the acceleration due to gravity on the surface of Mars if its radius is $3.4 \times 10^6 \, \text{m}$ and mass is $6.42 \times 10^{23} \, \text{kg}$?

    • Answer:
      $g = \frac{GM}{R^2}$
      Substituting the values, $g \approx 3.71 \, \text{m/s}^2$.

24. Calculate the height at which the value of ‘g’ becomes 4.9 $\text{m/s}^2$.

    • Answer: Use $g' = g \left( \frac{R}{R + h} \right)^2$.

25. If the mass of Earth is doubled and its radius is halved, what will be the new acceleration due to gravity?

    • Answer: $g' = 8g$.

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4. Long Answer Questions (5 Marks)

26. Derive the expression for acceleration due to gravity on the surface of a planet.
27. State and derive the formula for escape velocity.
28. Explain Kepler’s laws of planetary motion with mathematical expressions.
29. Derive the expression for gravitational potential energy.
30. Explain the variation of ‘g’ with latitude on Earth.
31. Derive the expression for orbital velocity of a satellite.
32. Discuss the concept of weightlessness in an orbiting satellite.
33. Explain the energy of a satellite in orbit.
34. How does the gravitational force vary with mass and distance?
35. Calculate the gravitational potential energy of a system of two masses separated by a distance r.

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5. Higher Order Thinking Skills (HOTS) Questions

36. Why is the value of g zero at the center of the Earth?

    • Answer: At the center, the gravitational forces from all directions cancel out.

37. Why don’t we feel the gravitational pull of the Moon?

    • Answer: The gravitational pull is too small compared to Earth’s gravity.

38. If the Moon were twice as far from the Earth, how would its gravitational pull change?

    • Answer: The gravitational force would reduce to one-fourth.

39. Why does a satellite in a higher orbit have a longer period?

    • Answer: As altitude increases, the orbital velocity decreases, leading to a longer period.

40. Why do astronauts feel weightless even though gravity acts on them?

    • Answer: They are in free fall along with the spacecraft.

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6. Assertion-Reason Type Questions

41. Assertion (A): The value of ‘g’ decreases with depth.
    Reason (R): The mass contributing to gravitational pull decreases with depth.

    • Answer: Both A and R are true, and R is the correct explanation.

42. Assertion (A): Geostationary satellites appear stationary from Earth.
    Reason (R): They revolve with the same angular velocity as the Earth.

    • Answer: Both A and R are true, and R is the correct explanation.

43. Assertion (A): The Moon has no atmosphere.
    Reason (R): The escape velocity on the Moon is low.

    • Answer: Both A and R are true, and R is the correct explanation.

44. Assertion (A): The gravitational force between two bodies depends only on their masses.
    Reason (R): It is independent of the medium between the bodies.

    • Answer: Both A and R are true, and R is the correct explanation.