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. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

The correct option is D $4$

Escape velocity $v_e=\sqrt{\frac{2GM}{R}}$
$\therefore \frac{v_1}{v_2}=\frac{\sqrt{\frac{2GM}{R}}}{\sqrt{\frac{\frac{2GM}{2}}{\frac{R}{2}}}}=1=\frac{n}{4}$
$\Rightarrow n=4$