The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

Solution

Physics sir · 3 steps

Mass stays fixed, so g depends only on 1/R²: halve the radius and g goes up four times.

1. Surface gravity. At the surface, g = GM/R², where R is the radius of the earth. With M fixed, g is proportional to 1/R².
2. New radius. Halving the diameter halves the radius too, so the new radius is R' = R/2.

   g' = GM/(R/2)² = 4 GM/R² = 4g

3. So. The acceleration due to gravity becomes 4g, which is option (d).

The idea to keep. For surface gravity, write g = GM/R² and ask what changes. Mass fixed means g ∝ 1/R², so any change in radius shows up squared.

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