If the radius of a planet is R and density is | vedclass

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(C) The formula for escape velocity is $v_{e} = \sqrt{\frac{2GM}{R}}$.Since the mass $M$ of a planet can be expressed in terms of its density $\rho$ a

Vedclass · Accepted Answer

$R \sqrt{\rho}$

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(C) The formula for escape velocity is $v_{e} = \sqrt{\frac{2GM}{R}}$.Since the mass $M$ of a planet can be expressed in terms of its density $ho$ and radius $R$ as $M = 	ext{Volume} 	imes 	ext{density} = \frac{4}{3} \pi R^{3} ho$.Substituting this into the escape velocity formula:$v_{e} = \sqrt{\frac{2G}{R} 	imes \frac{4}{3} \pi R^{3} ho} = \sqrt{\frac{8}{3} G \pi R^{2} ho}$.Simplifying the expression,we get $v_{e} = R \sqrt{\frac{8}{3} G \pi ho}$.Since $\frac{8}{3}$,$G$,and $\pi$ are constants,we find that $v_{e} \propto R \sqrt{ho}$.

If the radius of a planet is $R$ and density is $\rho$,then the escape velocity $v_{e}$ of any body from its surface will be proportional to:

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