Question

The ratio of escape velocities of two planets if $g$ values on the two planets are $9.9$ m/s${}^2$ and $3.3$ m/s${}^2$ and their radii are $6400km$ and $3400km$ respectively is

• A. $2.36:1$
• B. $1.36:1$
• C. $3.36:1$
• D. $4.36:1$

Answer 1

The correct option is A $2.36:1$

Escape speed, $v_e=\sqrt{2gR}$

$\Rightarrow \frac{v_2}{v_1}=\sqrt{\frac{g_2{R}_2}{g_1{R}_1}}=\sqrt{\frac{9.9\times 6400}{3.3\times 3400}}=2.37$

$\Rightarrow v_2:v_1=2.37:1$