Physics - Gravitation Question with Solution | TestHub

The escape velocity from the surface of a planet is given by the formula $v_e=\sqrt{\frac{2GM}{R}}$. For Planet A, $v_A=\sqrt{\frac{2GM}{R}}$. For Planet B, with mass $M_B=2M$ and radius $R_B=R/2$, the escape velocity is $v_B=\sqrt{\frac{2G(2M)}{R/2}}=\sqrt{\frac{8GM}{R}}$. We can rewrite this as $v_B=\sqrt{4\times \frac{2GM}{R}}=2\sqrt{\frac{2GM}{R}}$. Therefore, $v_B=2v_A$.