JEE MAIN - Physics (2022 - 29th June Morning Shift - No. 13)
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 :
12 kms$$-$$1
24 kms$$-$$1
36 kms$$-$$1
6 kms$$-$$1
Explanation
$${v_{esc}} - \sqrt {{{2GM} \over R}} = \sqrt {{{2G} \over R} \times \rho \times {4 \over 3}\pi {R^3}} $$
$$ \Rightarrow {v_{esc}} \propto R\sqrt \rho $$
$$ \Rightarrow {{{{({v_{esc}})}_B}} \over {{{({v_{esc}})}_A}}} = 1$$
$$ \Rightarrow {({v_{esc}})_B} = 12$$ km/s
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