JEE Main 2023 · 1 February · morning · Single correct · +4 / −1
Given below are two statements:
Statement I: Acceleration due to gravity is different at different places on the surface of earth.
Statement II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below
- (a) Both Statement I and Statement II are true
- (b) Both Statement I and Statement II are false
- (c) Statement I is false but Statement II is true
- (d) Statement I is true but Statement II is false
Answer and solution
Answer (d) Statement I is true but Statement II is false
Solution
Physics sir · 4 steps
On the surface g changes with latitude, but going down you lose the mass below you, so g falls.
- Statement I. Earth spins and bulges at the equator, so g depends on where you stand. At latitude λ, g' = g - ω² R cos² λ. At the poles g is largest, and at the equator it is about 0.034 m s⁻² smaller. So Statement I is true.
- Going below. At depth d, only the sphere of radius R - d under you pulls you. For a uniform earth its mass is M(R-d)³/R³, so g_d = GM(R-d)/R³.
g_d = g(1 - d/R)
- Statement II. As d grows, g_d gets smaller, and it becomes zero at the centre (d = R). Gravity decreases with depth, so Statement II is false.
- So. Statement I is true and Statement II is false, which is option (d).
The idea to keep. Below the surface, only the mass inside your radius pulls you, so g falls linearly to zero at the centre. On the surface, g is largest at the poles and smallest at the equator.
Answer from the NTA final answer key. Solution by PrepWiser.