Gravitation Olympiad (Class 10 Science)

NSO and advanced physics olympiad questions on gravity, planetary motion, and orbital mechanics. Requires mastery of Newton's law and orbital concepts.

Gravitation Olympiad (Class 10 Science)

NSO and advanced physics olympiad questions on gravity, planetary motion, and orbital mechanics. Requires mastery of Newton's law and orbital concepts.

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TL;DR: NSO and advanced physics olympiad questions on gravity, planetary motion, and orbital mechanics. Requires mastery of Newton's law and orbital concepts…

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NSO and advanced physics olympiad questions on gravity, planetary motion, and orbital mechanics. Requires mastery of Newton's law and orbital concepts.

Gravitation Olympiad MCQs with Answers & Explanations

Q1. The gravitational force between two objects is F. If the distance between them is halved, what is the new force?

  1. F/4
  2. 4F ✓ (correct)
  3. F/2
  4. 2F

Explanation: Gravitational force F = G*m1*m2/r^2. If r becomes r/2, new force = G*m1*m2/(r/2)^2 = 4*G*m1*m2/r^2 = 4F.

Q2. The weight of an object on Earth is 100 N. What is its weight on the Moon where g_moon = g_earth/6?

  1. 600 N
  2. 50 N
  3. 16.67 N ✓ (correct)
  4. 33.33 N

Explanation: Weight = m*g. On Moon: W_moon = m*g_earth/6 = (m*g_earth)/6 = 100/6 = 16.67 N.

Q3. A satellite orbits Earth at radius r with speed v. To achieve a stable orbit, what must be true?

  1. Centripetal force is zero
  2. They are independent
  3. Gravitational force exceeds centripetal force
  4. Gravitational force provides centripetal force ✓ (correct)

Explanation: For stable orbit, gravitational attraction provides exactly the centripetal force needed: G*M*m/r^2 = m*v^2/r.

Q4. If the mass of Earth doubled while its radius remained the same, how would g change?

  1. Become 2g ✓ (correct)
  2. Become g/4
  3. Remain g
  4. Become g/2

Explanation: g = G*M/r^2. If M doubles: g_new = G*2M/r^2 = 2*g.

Q5. An object is dropped from the top of a building on Earth (g=10 m/s^2). After 2 seconds, how far has it fallen?

  1. 10 m
  2. 20 m ✓ (correct)
  3. 30 m
  4. 40 m

Explanation: Starting from rest, s = ½gt² = ½ x 10 x 2² = 20 m.

Q6. The escape velocity from Earth is 11.2 km/s. What is the escape velocity from a planet with double Earth's mass and double its radius?

  1. 22.4 km/s
  2. 5.6 km/s
  3. 11.2 km/s ✓ (correct)
  4. 7.9 km/s

Explanation: v_escape = sqrt(2*G*M/r). If M doubles and r doubles: v_escape_new = sqrt(2*G*2M/2r) = sqrt(2*G*M/r) = v_escape (unchanged).

Q7. A planet has density 2 times that of Earth and radius 1/2 times Earth's radius. How does its surface gravity compare to Earth's?

  1. 2g
  2. g/2
  3. g/4
  4. g ✓ (correct)

Explanation: Surface gravity g = (4/3)πGρR, so g is proportional to ρR. Doubling density and halving radius gives 2 x ½ = 1, i.e. the same g.

Q8. Kepler's Third Law states that the square of the orbital period is proportional to the cube of the semi-major axis. For a satellite orbiting twice as far from Earth, how does its period change?

  1. sqrt(8) times larger ✓ (correct)
  2. Halved
  3. 8 times larger
  4. Same

Explanation: T^2 is proportional to a^3. If a doubles: T_new^2 proportional to (2a)^3 = 8*a^3. So T_new^2 = 8*T^2, giving T_new = T*sqrt(8) = 2*sqrt(2)*T.

Frequently Asked Questions

Why does gravity on the Moon's surface differ from Earth's despite both being planets?

Gravity at a surface depends on g = G*M/R^2, which depends on the planet's mass and radius. The Moon has much less mass than Earth (about 1/81), so gravitational force is weaker. Although the Moon is smaller (radius about 1/4 of Earth), its lower mass dominates, resulting in g_moon ≈ g_earth/6. Larger, denser planets have stronger surface gravity.

What is the difference between weight and mass?

Mass is the amount of matter in an object and remains constant everywhere. Weight is the force exerted by gravity on that mass, given by W = m*g. On Earth (g=10 m/s^2), a 10 kg object weighs 100 N. On the Moon (g=1.6 m/s^2), the same object weighs only 16 N. An astronaut's mass never changes, but their weight varies depending on the gravitational field they're in.

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