A body of mass $\mathrm{m}$ is projected with velocity $\lambda \,v_{\mathrm{e}}$ in vertically upward direction from the surface of the earth into space. It is given that $v_{\mathrm{e}}$ is escape velocity and $\lambda

Question

A body of mass $\mathrm{m}$ is projected with velocity $\lambda \,v_{\mathrm{e}}$ in vertically upward direction from the surface of the earth into space. It is given that $v_{\mathrm{e}}$ is escape velocity and $\lambda<1$. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be :

(R : radius of earth)

$\frac{\mathrm{R}}{1+\lambda^{2}}$

$\frac{R}{1-\lambda^{2}}$

$\frac{R}{1-\lambda}$

$\frac{\lambda^{2} \mathrm{R}}{1-\lambda^{2}}$

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