Q 11-07-038JEE MainMedium
With what minimum speed, in km/s, must a body be projected from the surface of a planet of mass $6 \times 10^{24}$ kg and radius $6.67 \times 10^6$ m to escape its gravity? ($G = 6.67 \times 10^{-11}\ \text{N m}^2\text{kg}^{-2}$; give the answer to the nearest whole number)
Numerical value type. Enter your answer.
Answer: 11
Concept. $v_e = \sqrt{\dfrac{2GM}{R}}$.
Step 1. Substitute.
$$v_e = \sqrt{\frac{2 \times 6.67 \times 10^{-11} \times 6 \times 10^{24}}{6.67 \times 10^6}} = \sqrt{1.2 \times 10^8} \approx 1.10 \times 10^4\ \text{m/s}$$
Answer. $11$.
Solution by Sreeraj P, M.Sc Physics