AIIMS 2017 Physics Gravitational Force MCQ Question

To determine the weight of an object on the new planet, we first calculate its radius using the relationship between mass (M), density (ρ), and volume (V). Given that the planet has double the mass of Earth (M = 2Mₑ) and the same average density (ρ = ρₑ), we find the volume is also doubled, leading to a radius R that is $R = (2)^{1/3} Rₑ$. The weight of an object is proportional to gravitational acceleration (g), which varies with radius as $g' = gₑ \left( \frac{M}{R^2} \right)$. Substituting the values gives $g' = gₑ \left( \frac{2Mₑ}{(2)^{2/3} Rₑ^2} \right) = 2^{1/3} gₑ$, resulting in a weight of $2^{1/3} W$ on the new planet. Options A, B, and C are incorrect as they do not account for the change in gravitational acceleration due to the altered radius and mass relationship.