The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Rₑ=6400 km) :

Solution

Physics sir · 3 steps

Weight falls as the square of distance from the centre, so measure from the centre, not the surface.

1. Distance from centre. Gravity depends on distance from the centre of the earth. At the surface that distance is Rₑ = 6400 km. At the altitude it is Rₑ + h = 6400 + 3200 = 9600 km.

   Wₕ = W₀(Rₑ/(Rₑ + h))²

2. Put in numbers. The ratio is 6400/9600 = 2/3, and its square is 4/9. So Wₕ = 18 × 4/9 N.
3. So. Wₕ = 8 N, which is option (d).

The idea to keep. For any height above the surface, use gₕ = g(R/(R+h))². The shortcut g(1 - 2h/R) works only when h is much smaller than R, and here h = R/2 is not small.

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