The approximate height from the surface of earth at which the weight of the body becomes 1/3 of its weight on the surface of earth is :
[Radius of earth R = 6400 km and √3 = 1.732]

Solution

Physics sir · 3 steps

One third the weight means √3 times the distance from the centre, not from the surface.

1. Weight follows g. Mass does not change, so weight goes down exactly as g does. Above the surface, g falls with the square of the distance from the centre of the earth.

   gₕ = g R²/(R+h)² = g/3

2. Solve for h. This gives (R+h)² = 3R², so R + h = √3 R. Then h = (√3 - 1)R = 0.732 × 6400 km = 4684.8 km.
3. So. The height is about 4685 km, which is option (b).

The idea to keep. The shortcut gₕ ≈ g(1 - 2h/R) works only when h is much smaller than R. For a big change in weight, use the exact R²/(R+h)² form.

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