A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be :

Solution

Physics sir · 3 steps

Measure distance from the centre of the Earth: height 9R puts the body at 10R, so the weight falls by 10².

1. Inverse square law. Weight is mg, and above the surface g falls as 1/r², where r is the distance from the centre of the Earth, not from the surface.
2. Find the distance. At height h = 9R, the body is r = R + 9R = 10R from the centre.

   W'/W = (R/(R+h))² = (R/10R)² = 1/100

3. So. The weight at that height is W/100, which is option (c).

The idea to keep. For a height above the surface, always add R first, then apply the inverse square. g depends on (R+h)², never on h² alone.

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