A planet has a mass M₁ and radius R₁. The value of acceleration due to gravity on its surface is g₁. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?

The correct answer is C, g₁/2. Surface gravity is g = GM/R², so doubling the mass doubles g while doubling the radius divides it by four, leaving g₁ × 2/4 = g₁/2.

For planet 2, g₂ = G(2M₁)/(2R₁)² = 2GM₁/4R₁² = ½ × GM₁/R₁². The key point is that g depends on the square of the radius but only on the first power of the mass. That is why a larger planet does not always have stronger gravity at its surface: Uranus is about 14 times as massive as the Earth, yet its surface gravity is slightly less than the Earth's because its radius is about four times larger.

A is wrong because g would stay the same only if the mass rose four times along with a doubled radius.

B is wrong because it counts the doubled mass but ignores the larger radius.

D is wrong because it counts the larger radius but ignores the doubled mass.

Exam tip: g = GM/R²; mass ×2 gives g ×2, radius ×2 gives g ÷4.