Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

Solution

Physics sir · 3 steps

Same density means the radius grows with the mass, and that bigger radius pulls g back down.

1. Write g using density. Put M = 4/3π R³ ρ into g = GM/R². This gives g = 4/3π G ρ R, so at fixed density g is proportional to R.
2. Find the new radius. At the same density, mass is proportional to volume, so M ∝ R³. Doubling the mass makes R'³ = 2R³, so R' = 2^(1/3)R.

   g'/g = R'/R = 2^(1/3) (check: M'/M(R/R')² = 2 × 2^(-2/3) = 2^(1/3))

3. So. Weight is mg and the mass of the object does not change. Its weight on the planet is 2^(1/3)W, which is option (c).

The idea to keep. At fixed density, g = 4/3π Gρ R, so g ∝ R ∝ M^(1/3). Whenever density is held fixed, turn mass into radius first and let the radius decide g.

Answer from the NTA final answer key. Solution by PrepWiser.