Q71 / 90 · JEE Main 2021 (25 Jul Shift 2) · Physics

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:

Solution

Density is same

$M = \frac{4}{3} π R^{3} ρ, 2 m = \frac{4}{3} π R^{' 3} ρ$

$R^{'} = 2^{\frac{1}{3}} R$

$W = \frac{G M m}{R^{2}}$

$W_{2} = \frac{G 2 M m}{R^{' 2}}$

$W_{2} = 2^{\frac{1}{3}} W$

Hence, the correct answer is option: 'C'.