AimMent
Exam level3 past questions

Acceleration due to gravity and its variation

Acceleration due to gravity (g) is the acceleration experienced by a body due to Earth's gravity, and it varies with height, depth, and planetary properties.

Why this shows up in the exam

You must understand how g changes with location and how it affects motion and energy calculations in NEET.

How NEET tests this

Numerical · 5 QsApplication · 2 Qs

Learn the idea

g is the acceleration a body feels due to Earth's pull; it changes with distance from the centre and with any additional acceleration of the reference frame. The key insight is that g varies as the inverse square of the distance from the centre (or linearly with depth for a uniform sphere).

🧠 Memory hook: Gravity falls like a shrinking shadow – double the distance and the shadow (g) shrinks to one‑fourth.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • g = GM/R² at the Earth's surface
  • g at height h: g = g₀·(R²/(R+h)²)
  • g inside a uniform Earth at distance r from centre: g = g₀·(r/R)
  • g can be written as g = (4/3)πGρR for a body of uniform density ρ
  • Effective gravity in an accelerating frame: g_eff = g ± a (sign depends on direction of a)

How to approach it

  1. 1Read the question and decide which situation applies – surface, above the surface, inside the Earth or a non‑inertial frame.
  2. 2Write the appropriate formula from the key ideas; substitute given quantities (use ρR relation when density is given).
  3. 3If the frame accelerates, add (or subtract) the acceleration to g to get g_eff.
  4. 4Check the sign and whether the result should increase or decrease the quantity asked (e.g., period of a pendulum).

Worked example — watch it click

A seconds pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

  • A)comes down with uniform acceleration.
  • B)moves round the Earth in a geostationary orbit.
  • C)moves up with a uniform velocity.
  • ✅moves up with uniform acceleration.

The concept behind this problem

The pendulum problem checks whether you recognise that an upward accelerating rocket increases the effective gravity, making the period shorter.

Step by step

  1. 1Period T = 2π√(L/g_eff).
  2. 2When rocket moves up with uniform acceleration a, effective gravity g_eff = g + a increases.
  3. 3Therefore period T decreases.
  4. 4Options: (a) coming down with acceleration reduces g_eff, increases T;
  5. 5(b) geostationary orbit has g_eff ≈ 0, increases T;
  6. 6(c) uniform velocity doesn't change g_eff;
  7. 7(d) moving up with acceleration increases g_eff, decreases T.
  8. 8Answer is (d).

Watch out

Students often think moving up reduces g, forgetting that the rocket’s upward acceleration adds to the gravitational pull.

Common slip-ups that cost marks

  • •Confusing upward acceleration with a reduction of g – upward a adds to g, downward a subtracts.
  • •Using the surface value g₀ when the problem involves height or depth; always replace with the distance‑dependent formula.
  • •Assuming the Earth’s density is uniform unless the problem states otherwise; the ρ‑R relation is only valid for a uniform sphere.

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 3NEET 2023

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3π / Gd represents:

Push further

More challenging

3 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 3

An astronaut lands on a planet where the escape velocity is twice that of Earth. If the planet's radius is the same as Earth's, what is the acceleration due to gravity on the planet's surface compared to Earth's (g_e)?

More from Gravitation