Question

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is $v$, then the escape velocity from the planet is :

• A. $\sqrt{3}v$
• B. $\sqrt{2}v$
• C. $v$
• D. $\sqrt{5}v$

Answer 1

The correct option is A

$\sqrt{3}v$

Escape velocity from the earth $v_e=\sqrt{\frac{2GM}{R}}$

For a given planet, $v_p=\sqrt{\frac{2G{M}_P}{R_P}}$

=$\sqrt{\frac{2G\left(6M\right)}{2R}}$

=$\sqrt{3}{v}_e$

=$\sqrt{3}v$