Question

If a planet has twice the mass of earth and three times the radius $(R)$ of earth, then the escape velocity of the planet is (${\upsilon }_e$ = escape velocity of earth)

• A. $\sqrt{\frac{1}{2}}{\upsilon }_e$
• B. $\sqrt{\frac{2}{3}}{\upsilon }_e$
• C. $\sqrt{2}{\upsilon }_e$
• D. none of these

Answer 1

Answer: (B)

Escape velocity,${\upsilon }_e=\sqrt{2gR}$
$=\sqrt{\frac{2GM}{R^2}}R$ $\left(\because g=\frac{GM}{R^2}\right)$
$\therefore {\upsilon }_e\propto \sqrt{\frac{M}{R}}$ ...(i)
Given, $M_p=2M$ and $R_p=3R$
$\therefore ({\upsilon }_e{)}_p=\sqrt{\frac{2}{3}}{\upsilon }_e$ (Using (i))