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  4. A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. Its radius in terms of radius of earth R will be

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Q. A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. Its radius in terms of radius of earth $R$ will be

Gravitation

Solution:

It is given that, the density of planet is twice the density of earth and both of them have same acceleration due to gravity.
if $g$ and $g^{\prime}$ are the acceleration due to gravity of earth and planet, then $g=g^{\prime}$
$\therefore \frac{G}{R^{2}}\left[\frac{4}{3} \pi R^{3} \rho\right]=\frac{G}{R^{\prime 2}} \times \frac{4}{3} \pi R^{\prime 3}(2 \rho)$
$\Rightarrow R^{\prime}=\frac{R}{2}$