Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth d=R/2 from the surface of earth, if its weight on the surface of earth is 200 N, will be:
(Given R = radius of earth)

Solution

Physics sir · 4 steps

Going down, only the earth below you pulls, so g drops in a straight line with depth.

1. Gravity inside earth. At depth d the body is pulled only by the sphere of radius R - d beneath it. For uniform density, g at that point falls linearly with depth.

   g_d = g(1 - d/R)

2. Put in numbers. With d = R/2, the bracket is 1 - 1/2 = 1/2. So g_d = g/2.
3. Weight follows g. Mass does not change, so weight scales with g: W_d = 1/2 × 200 N = 100 N.
4. So. The body weighs 100 N at depth R/2, which is option (a).

The idea to keep. Inside a uniform earth, g falls linearly: g_d = g(1 - d/R), reaching zero at the centre. Do not mix it up with height, where g falls as 1/r².

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