Question

The radius of planet A is half the radius of planet B. If the mass of A is $M_A$, what must be the mass of B so that value of g on B is half that of its value on A?

Answer 1

$g=\frac{GM}{R^2}$

$⟹M=\frac{g{R}^2}{G}$

Here, $\frac{g_B}{g_A}=\frac{1}{2}$

and $\frac{R_B}{R_A}=2$

$⟹\frac{M_B}{M_A}=\frac{g_B}{g_A}{\left(\frac{R_B}{R_A}\right)}^2$

$⟹\frac{M_B}{M_A}=\frac{1}{2}{\left(2\right)}^2$

$⟹M_B=2M_A$