A body is projected vertically from the surface of the earth of radius ‘ R ’ with velocity equal to half of the escape velocity. The maximum height reached by the body is

Step-by-step solution

From mechanical energy conservation k i + U i = k f + U f ⇒ 1 2 m . 2 G M 4 R - G M m R = 0 - G M m r ∵ v e = 2 G M R ⇒ - 3 4 . G M m R = - G M m r ⇒ r = 4 r 3 ⇒ R + h = 4 R 3 h = R 3