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Question

(C) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{4}{3} \pi G \rho R$,where $\rho$ is the density

Vedclass · Accepted Answer

It is doubled.

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(C) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{4}{3} \pi G \rho R$,where $\rho$ is the density and $R$ is the radius of the planet.Since $G$,$\pi$,and $R$ are constant,we have $g \propto \rho$.If the density $\rho$ is doubled,the new acceleration due to gravity $g'$ becomes $g' = \frac{4}{3} \pi G (2\rho) R = 2g$.Therefore,the value of $g$ on the planet is doubled.

If the density of a planet is doubled without changing its radius,how does $g$ on the planet change?

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