The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).

Solution

Physics sir · 3 steps

Measure distance from the centre of the earth, not from the surface: P is at 3R, not 2R.

1. Distance from centre. The height is the diameter, so h = 2R. Gravity depends on the distance from the earth's centre, which is r = R + h = 3R.

   g' = GM/(R+h)² = g(R/(R+h))²

2. Put in numbers. g' = g(R/3R)² = g × 1/9.
3. So. The acceleration due to gravity at P is g/9, option (d).

The idea to keep. Above the surface, g falls as 1/r² with r measured from the earth's centre. Always add R to the height before you square.

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