The escape velocity of a body from a planet o | vedclass

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(A) The formula for escape velocity $v_e$ is given by $v_e = \sqrt{\frac{2GM}{R}}$.Given for the first planet: $v_{e1} = \sqrt{\frac{2GM}{R}} = 14 \,k

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$7$

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(A) The formula for escape velocity $v_e$ is given by $v_e = \sqrt{\frac{2GM}{R}}$.Given for the first planet: $v_{e1} = \sqrt{\frac{2GM}{R}} = 14 \,km \,s^{-1}$.For the second planet,the mass is $M$ and the diameter is $8R$,so the radius $R' = \frac{8R}{2} = 4R$.The escape velocity for the second planet is $v_{e2} = \sqrt{\frac{2GM}{R'}} = \sqrt{\frac{2GM}{4R}}$.This can be written as $v_{e2} = \frac{1}{\sqrt{4}} \sqrt{\frac{2GM}{R}} = \frac{1}{2} v_{e1}$.Substituting the value of $v_{e1}$: $v_{e2} = \frac{14}{2} = 7 \,km \,s^{-1}$.

The escape velocity of a body from a planet of mass $M$ and radius $R$ is $14 \,km \,s^{-1}$. The escape velocity of the body from another planet having same mass and diameter $8R$ (in $km \,s^{-1}$) is

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