Question

The escape velocity from the Earth's surface is $v.$ The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

• A. $4v$
• B. $v$
• C. $2v$
• D. $3v$

Answer 1

The correct option is A $4v$

Escape velocity from the Earth's surface,

$v_e=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2G[\rho \times (4\pi R^3/3\left)\right]}{R}}$

$\Rightarrow v_e=\sqrt{\frac{8G\rho \pi R^2}{3}}$

$\therefore v_e\propto R\text{(For same density)}$

$\frac{v_1}{v_2}=\frac{R_1}{R_2}\Rightarrow \frac{v}{v_2}=\frac{R}{4R}$

$\therefore v_2=4v$

Hence, option $\left(\text{A}\right)$ is correct.