A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:

Solution

Physics sir · 4 steps

Same density means a bigger planet has a bigger radius, and g grows with the radius, not with the mass alone.

1. Write g with density. Put M = 4/3π R³ ρ into g = GM/R². One power of R survives, so with ρ fixed, g is proportional to R.

   g = GM/R² = 4/3π G ρ R

2. Find the new radius. With the same density, mass is proportional to R³. Doubling the mass makes R³ twice as large, so Rₚ = 2^(1/3) Rₑ.
3. Compare g. Since g ∝ R, gₚ = 2^(1/3) gₑ. You get the same result from g ∝ M/R²: 2/(2^(1/3))² = 2^(1/3).
4. So. Weight is mg and the mass of the object does not change, so it weighs 2^(1/3) W on the planet. The answer is (d).

The idea to keep. When density is fixed, use g = 4/3π Gρ R, so g ∝ R. Find how the radius changes from M ∝ R³, and g changes by the same factor.

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