The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

Solution

Physics sir · 3 steps

Below the surface g falls linearly with depth, so going halfway down cuts the weight to half.

1. Why g drops. At depth d, only the mass inside the smaller sphere of radius R - d pulls on the body. The outer shell gives zero net force, so g falls in proportion to the remaining distance from the centre.

   g_d = g(1 - d/R)

2. Put in d. With d = R/2, g_d = g(1 - 1/2) = g/2. The mass of the body does not change, so its weight mg also becomes half.
3. So. New weight = 1/2 × 400 N = 200 N, option (b).

The idea to keep. Inside the earth, g_d = g(1 - d/R) falls linearly to zero at the centre. Outside, it falls as 1/r². Check which side of the surface you are on first.

Answer from the NTA final answer key. Solution by PrepWiser.