Question

Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius, that 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. $4$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $4$

Escape velcity of the planet $A$ is,

$V_A=\sqrt{\frac{2G{M}_A}{R_A}}$

Where, $M_A$ and $R_A$ be the mass and radius of the planet $A$.

According to given information,

$M_B=\frac{M_A}{2},R_B=\frac{R_A}{2}$

$\therefore V_B=\sqrt{\frac{2G\frac{M_A}{2}}{\frac{R_A}{2}}}=\sqrt{\frac{2G{M}_A}{R_A}}=V_A$

Now, $\frac{V_A}{V_B}=\frac{n}{4}=1$

$\Rightarrow n=4$

Hence, $\left(A\right)$ is the correct answer.