Gravitation

JEE Main level, single correct, medium

115 of 223

Question 115 of 223

Escape velocity of a body from earth is 11.2kms−111.2km{s}^{-1}. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

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Answer: (D) 7.9kms−17.9km{s}^{-1}

Given: RP=RE3,MP=ME6{R}_{P}=\dfrac{{R}_{E}}{3},{M}_{P}=\dfrac{{M}_{E}}{6}
Escape velocity is given by, v=2GMRv=\sqrt{\dfrac{2GM}{R}}
Therefore,
vE=2GMERE...(i){v}_{E}=\sqrt{\dfrac{2G{M}_{E}}{{R}_{E}}}...(i)
vP=2GMPRP...(ii){v}_{P}=\sqrt{\dfrac{2G{M}_{P}}{{R}_{P}}}...(ii)
⇒vEvP=2\Rightarrow \dfrac{{v}_{E}}{{v}_{P}}=\sqrt{2}
⇒vP=vE2=11.22=7.9kms−1\Rightarrow {v}_{P}=\dfrac{{v}_{E}}{\sqrt{2}}=\dfrac{11.2}{\sqrt{2}}=7.9km{s}^{-1}

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