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))