Question

Planet $A$ has mass $M$ and radius $R$, planet $B$ has mass $M/3$ and radius $3R$. If escape velocity from planet $A$ is $V_e$, then escape velocity from planet $B$ will be

• A. $\frac{V_e}{3}$
• B. $3V_e$
• C. $\frac{V_e}{2}$
• D. $\frac{2V_e}{3}$

Answer 1

The correct option is A $\frac{V_e}{3}$

We know that escape velocity at any planet is $\sqrt{\frac{2GM}{R}}$, where $M$ is the mass of that planet and $R$ is the radius.

$\Rightarrow V_A=\sqrt{\frac{2GM}{R}}$
$\Rightarrow V_B=\sqrt{\frac{2G\left(\frac{M}{3}\right)}{3R}}=\sqrt{\frac{2GM}{9R}}=\frac{V_A}{3}$
$V_B=\frac{V_e}{3}$