Question

b. 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?

Answer 1

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

⇒$M=\frac{g{R}^2}{G}$ 

Acording to the given data , $\frac{gB}{gA}=\frac{1}{2}$

and $\frac{R_B}{R_A}=2$ 

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

⇒$\frac{M_B}{M_A}=\frac{1}{2}{2}^2$

⇒$M_B=2M_A$

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