A body of mass m is projected with velocity λ ve 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)

(D) \frac{\lambda^{2} R}{1-\lambda^{2}}

JEE Mains · Physics · STD 11 - Gravitation

A body of mass \(m\) is projected with velocity \(\lambda v_{e}\) in vertically upward direction from the surface of the earth into space. It is given that \(v _{ e }\) is escape velocity and \(\lambda<1\). 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)

Pick an option to check your answer.

Verified Solution

Correct Answer

(B) \(\frac{R}{1-\lambda^{2}}\)

Detailed explanation

\(-\frac{ GMm }{ R }+\frac{1}{2} m \lambda^{2} V _{ e }^{2}=-\frac{ GMm }{ h }\)

\(-\frac{ GMm }{ R }+\frac{1}{2} \lambda^{2} \frac{2 GMm }{ R }=-\frac{ GMm }{ h }\)

\(\frac{\lambda^{2}}{ R }-\frac{1}{ R }=\frac{-1}{ h }\)

\(\frac{1}{ h }=\frac{1-\lambda^{2}}{ R }\)

\(h =\frac{ R }{1-\lambda^{2}}\)

Same subject

From JEE Mains