If the mass of the Earth were doubled and its radius halved, what would be the weight of a body of mass "m" on its surface? (Take "g" as the acceleration due to gravity on the unchanged Earth.)
- A0.5mg
- B4mg
- C8mg
- Dmg
Show answer and explanation
Correct answer: (c) 8mg
Explanation
On a planet's surface, g = GM/R².
If the mass becomes 2M and the radius R/2:
- new g = G(2M)/(R/2)² = 2GM ÷ (R²/4) = 8GM/R² = 8g.
The mass of the body stays m, so its weight becomes m × 8g = 8mg. Halving the radius has a larger effect than doubling the mass, because g depends on 1/R².