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  4. If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that of the earth, the gravitational acceleration on the surface of the planet is

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Q. If the density of a small planet is the same as that of earth, while the radius of the planet is $0.2$ times that of the earth, the gravitational acceleration on the surface of the planet is

Gravitation

Solution:

We know that,
$g=\frac{G M}{R^2}=\frac{G\left(\frac{4}{3} \pi R^3\right) \rho}{R^2}=\frac{4}{3} \pi G R \rho$
$\frac{g^{\prime}}{g}=\frac{R^{\prime}}{R}=\frac{0.2 R}{R}=0.2$
$ \therefore g^{\prime}=0.2 \,g$