Q 11-07-117JEE MainJEE Main 2022 (24 Jun, Shift 1)Easy
The approximate height from the surface of earth at which the weight of the body becomes $\dfrac{1}{3}$ of its weight on the surface of earth is: [Radius of earth $R = 6400\ \text{km}$ and $\sqrt3 = 1.732$]
Answer: (B) $4685\ \text{km}$
$$g' = \frac{gR^2}{(R+h)^2} = \frac{g}{3}\ \Rightarrow\ R + h = \sqrt3 R$$
$$h = (\sqrt3 - 1)R = 0.732\times 6400 \approx 4685\ \text{km}$$
Solution by Sreeraj P, M.Sc Physics