JEE Main 2022 · 27 June · morning · Single correct · +4 / −1
Given below are two statements :
Statement I : The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
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 true but Statement II is false
- (d) Statement I is false but Statement II is true
Answer and solution
Answer (a) Both Statement I and Statement II are true
Solution
Physics sir · 4 steps
At the centre, Earth pulls you equally from every side, so the pulls cancel and your weight is zero.
- Statement I. Newton's law F = (G m₁ m₂)/r² is a universal law. It acts between every pair of masses: two planets, an apple and the Earth, or two pebbles. For small masses the force is tiny, but it is never absent. So Statement I is true.
- Gravity inside Earth. At a depth d below the surface, only the mass inside radius R - d pulls you towards the centre. The shell of mass above you pulls you equally in all directions, so its net pull is zero. This makes g decrease linearly as you go down.
g_d = g(1 - d/R)
- At the centre. Put d = R. Then g_d = g(1 - 1) = 0, so the weight mg_d = 0. Your mass m is unchanged, but nothing is left to pull you in any one direction. So Statement II is true.
- So. Both statements are true, which is option (a).
The idea to keep. Mass never changes, but weight is mg, and g changes with position. Going down into Earth, g falls linearly and becomes zero at the centre.
Answer from the NTA final answer key. Solution by PrepWiser.