Physics - Gravitation Question with Solution | TestHub

The escape speed of a planet of mass $M$ and radius $R$ is given by $v=\sqrt{\frac{2GM}{R}}$.

For planet $P_1$, the escape speed is $v_1=\sqrt{\frac{2GM}{R_1}}$.

For planet $P_2$, the escape speed is $v_2=\sqrt{\frac{2GM}{R_2}}$.

Taking the ratio of the escape speeds:

$\frac{v_2}{v_1}=\sqrt{\frac{R_1}{R_2}}$

Given that $R_2=\frac{R_1}{2}$, substituting this into the equation gives:

$\frac{v_2}{v_1}=\sqrt{\frac{R_1}{\frac{R_1}{2}}}=\sqrt{2}$

Answer: $\sqrt{2}$