Q 11-07-156JEE MainJEE Main 2021 (25 Jul, Shift 2)Easy
Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is $W$, the weight of the same object on that planet will be:
Answer: (C) $2^{\frac{1}{3}}W$
$g = \dfrac{GM}{R^2} = \dfrac{4}{3}\pi G\rho R$, so at equal density $g \propto R$.
Equal density and double mass: $R'^3 = 2R^3 \Rightarrow R' = 2^{1/3}R$.
Hence $g' = 2^{1/3}g$ and the weight is $2^{1/3}W$.
Solution by Sreeraj P, M.Sc Physics