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Gravitation

JEE Main level, single correct, medium

118 of 223

Question 118 of 223

A planet having mass $9{M}_{e}$ and radius $4{R}_{e},$ where ${M}_{e}$ and ${R}_{e}$ are mass and radius of earth respectively, has escape velocity in $km{s}^{-1}$ given by: (Given escape velocity on earth ${V}_{e}=11.2\times {10}^{3}m{s}^{-1}$ )

Show answer and solution

Answer: (B) $16.8$

The escape velocity on earth is given by

{V}_{\text{e}}=\sqrt{\dfrac{2G{M}_{e}}{{R}_{e}}}

Escape velocity for the planet is

V{'}_{esc}=\sqrt{\dfrac{2G(9{M}_{e})}{4{R}_{e}}}...(i)

The escape velocity of earth is

{V}_{e}=11.2\times {10}^{3}m{s}^{-1}

From equation (i)

V{'}_{esc}=\sqrt{\dfrac{9}{4}\left(\dfrac{2G{M}_{e}}{{R}_{e}}\right)}=\dfrac{3}{2}\times 11.2\times {10}^{3}m{s}^{-1} \Rightarrow V{'}_{esc}=16.8km{s}^{-1}

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