Question

The ratio of escape velocity at earth $v_e$ to the escape velocity at a planet $v_p$ whose radius and mean density are twice as that of earth is :

• A. $1 : 2 \sqrt{2}$
• B. $1 : 4$
• C. $1 : \sqrt{2}$
• D. $1 : 2$

Answer 1

Answer: (A)

$1 : 2 \sqrt{2}$

Answer 2

$Ve = \sqrt{\frac{2GM}{R}} = \sqrt{\frac{2G}{R}.\left(\frac{4}{3} \pi R^{3}\rho\right)} \propto R\sqrt{\rho}$
$\therefore$ Ratio = $1 : 2 \sqrt{2}$