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Gravitation
Physics · Class 11NCERT pp. 127–1392 sets × 25 questions
Key facts and formulas for Gravitation, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Law of gravitation | F = G m₁m₂ / r²; g = GM/R²; GM = gR² |
| Kepler's laws | Orbit is an ellipse with the Sun at a focus; equal areas in equal times (r v constant); T² ∝ a³ |
| Variation of g | Height h: g′ = g R²/(R + h)² ≈ g(1 − 2h/R); depth d: g′ = g(1 − d/R); inside g ∝ r |
| Potential and energy | V = −GM/r; U = −GMm/r; V at surface = −gR; inside a shell V = −GM/R |
| Escape speed | v_e = √(2GM/R) = √(2gR) = 11.2 km/s; v_e = √2 × v_o |
| Satellite in circular orbit | v = √(GM/r); T = 2π√(r³/GM); surface-skimming: v = √(gR) = 7.9 km/s, T ≈ 85 min |
| Satellite energy | K = GMm/2r; U = −GMm/r; E = −GMm/2r; energy to free = GMm/2r |
| Geostationary satellite | T = 24 h, equatorial plane, west to east, r ≈ 6.6 R, height ≈ 36 000 km |
| Rotation of the Earth | Apparent g at the equator = g − R ω²; Rω² ≈ 0.034 m s⁻² |
| Tunnel through Earth | SHM with ω² = g/R, T = 2π√(R/g) ≈ 85 min; speed at the centre √(gR) |
Three sample questions
Q1. A planet is 2.0 × 10¹⁰ m from its star at the nearest point, moving at 40 km s⁻¹. At the farthest point, 8.0 × 10¹⁰ m away, its speed is
- 160 km s⁻¹
- 10 km s⁻¹
- 20 km s⁻¹
- 40 km s⁻¹
Hint and solution
Hint: Gravity is a central force, so the angular momentum of the planet about the star does not change. What stays constant, r times v?
- L = m r v = constant — Gravity acts along the line to the star, so there is no torque and angular momentum is conserved.
- r₁v₁ = r₂v₂ → 2 × 40 = 8 × v₂ — The mass cancels. Put distances in units of 10¹⁰ m and speeds in km per second.
- v₂ = (2 × 40) / 8 = 80 / 8 = 10 km s⁻¹ — Divide 80 by 8. The planet has slowed down because it is four times farther.
- Answer: 10 km s⁻¹ — So the speed at the farthest point is 10 kilometres per second. Option B.
Answer: B. Angular momentum is conserved, so r v is constant: 2 × 40 = 8 × v, giving v = 10 km s⁻¹.
Q2. Which statements about a planet going round the Sun are correct? (i) The Sun is at the centre of the elliptical orbit. (ii) The Sun-planet line sweeps equal areas in equal times. (iii) T² ∝ a³ for all planets of the Sun. (iv) The kinetic energy of the planet stays constant.
- (i) and (ii) only
- (i), (iii) and (iv)
- (iii) and (iv) only
- (ii) and (iii) only
Hint and solution
Hint: Recall the three laws one by one. Where exactly is the Sun in an ellipse, and does the planet keep a constant speed?
- Law 1: Sun at a focus of the ellipse — Statement (i) says the Sun is at the centre. That is wrong, it sits at a focus.
- Law 2: equal areas in equal times — Statement (ii) is exactly the second law, so it is true. It also tells us speed varies.
- Law 3: T² ∝ a³ for all planets — Statement (iii) is the third law for planets of the same star, so it is true.
- Speed changes, so K changes — Statement (iv) is false because the speed is larger near the Sun. So only (ii) and (iii) are correct. Option D.
Answer: D. The Sun is at a focus, not the centre (i is false). Speed changes along the ellipse (iv is false). Statements (ii) and (iii) are Kepler's second and third laws.
Q3. Assertion A: A planet moves fastest when it is nearest to the Sun. Reason R: The angular momentum of the planet about the Sun is conserved.
- Both A and R are true and R explains A
- Both A and R are true but R does not explain A
- A is true but R is false
- A is false but R is true
Hint and solution
Hint: Write angular momentum as m r v. If it stays constant and r gets smaller, what must happen to v? Then ask whether R gives the cause of A.
- L = m r v = constant — Gravity is a central force, so angular momentum about the Sun is conserved. R is true.
- Smaller r → larger v — Since m r v stays fixed, when r decreases the speed v must increase. So A is true.
- R gives the cause of A — The same conservation law is what produces the speed change, so R explains A. Both true and R explains A. Option A.
Answer: A. Since L = m r v is constant, a smaller r means a larger v. So R explains A.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.