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 the value of $g$ on $B$ is half that of its value on $A$?

• A. $M_A$
• B. $2M_A$
• C. $3M_A$
• D. $4M_A$

Answer 1

The correct option is B $2M_A$

Given,
$r_A=\frac{1}{2}{r}_B$ and $g_B=\frac{1}{2}{g}_A$
or, $\frac{G{M}_B}{r_B^2}=\frac{1}{2}\frac{G{M}_A}{r_A^2}$
or, $\frac{M_B}{4r_A^2}=\frac{1}{2}\frac{M_A}{r_A^2}$
or, $M_B=2M_A$