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

Question

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, R / 5, R / 3, R / 2, R / 4

MARKS App · Accepted Answer

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

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