"The escape velocity of a body on a planet 'A' is 12 kms$-$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :"

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$${v_{esc}} - \sqrt {{{2GM} \over R}} = \sqrt {{{2G} \over R} \times \rho \times {4 \over 3}\pi {R^3}} $$

$\Rightarrow {v_{esc}} \propto R\sqrt \rho$

$\Rightarrow {{{{({v_{esc}})}_B}} \over {{{({v_{esc}})}_A}}} = 1$

$\Rightarrow {({v_{esc}})_B} = 12$ km/s

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The escape velocity of a body on a planet 'A' is 12 kms^$-$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :

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The escape velocity of a body on a planet 'A' is 12 kms$-$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :

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The escape velocity of a body on a planet 'A' is 12 kms^$-$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :