A body of mass m is projected with velocity λ v e in vertically upward direction from the surface of the earth into space. It is given that v e is escape velocity and λ

Question

A body of mass m is projected with velocity λ v e in vertically upward direction from the surface of the earth into space. It is given that v e is escape velocity and λ < 1 . If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be ( R : radius of earth)

TestHub · Accepted Answer

Escape velocity is given by, v e = 2 G M e R e If the body goes to the height h from the surface of the earth, using mechanical energy conservation, ⇒ 1 2 m λ 2 G M e R e 2 - G M e m R e = - G M e m R e + h ⇒ λ 2 G M e m R e - G M e m R e = - G M e m R e + h ⇒ R e + h = R e 1 - λ 2

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