Question

Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius of Planet $A$. If the escape velocities from the Planets $A$ and $B$ are $v_A$ and $v_B$, respectively, then $\frac{v_{A}}{v_{B}}=\frac{n}{4}$. The value of $n$ is :

• A. $3$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (D)

$4$

Answer 2

$V_{e} = \sqrt{\frac{2GM}{R}}$ (Escape velocity)
$V_{A} = \sqrt{\frac{2GM}{R}}$
$V_{B} = \sqrt{\frac{2G\left[M/ 2\right]}{R/ 2}} = \sqrt{\frac{2GM}{R}}$
$\frac{V_{A}}{V_{B}} = 1 = \frac{n}{4} \Rightarrow n = 4$