Q 11-07-075JEE MainJEE Main 2024 (30 Jan, Shift 2)Easy
The escape velocity of a body from earth is $11.2\ \text{km s}^{-1}$. If the radius of a planet is one-third the radius of earth and its mass is one-sixth that of earth, the escape velocity from the planet is:
Answer: (D) $7.9\ \text{km s}^{-1}$
$v_e = \sqrt{\dfrac{2GM}{R}} \propto \sqrt{\dfrac MR}$
$$v_p = 11.2\sqrt{\frac{1/6}{1/3}} = \frac{11.2}{\sqrt2} \approx 7.9\ \text{km s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics