Two spherical planets $A$ and $B$ have same mass but densities in the ratio 8:1. For these planets, the ratio of acceleration due to gravity at the surface of $A$ to its value at the surface of $B$ is

Question

Dr. Abubacker · Accepted Answer

(c) Mass of two planets is same, so
$\frac{4}{3}\pi R_{1}^{3}\rho_{1} = \frac{4}{3}\pi R_{2}^{3}\rho_{2}$
or $\frac{R_{1}}{R_{2}} = \left( \frac{\rho_{2}}{\rho_{1}} \right)^{1/3} = \left( \frac{1}{8} \right)^{1/3} = \frac{1}{2}$
$\frac{g_{1}}{g_{2}} = \frac{GM/R_{1}^{2}}{GM/R_{2}^{2}} = \left( \frac{R_{2}}{R_{1}} \right)^{2} = (2)^{2} = 4$

Q. Two spherical planets $A$ and $B$ have same mass but densities in the ratio 8:1. For these planets, the ratio of acceleration due to gravity at the surface of $A$ to its value at the surface of $B$ is

Explanation

Reviewed by Dr. Abubacker

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