JEE Class main Answered

Acceleration due to gravity g = G ( M / R² )

where G is universal gravitational constant , M is mass of earth and R is radius of earth.

If consider earth as sphere of radius R and ρ is its density , then

Mass M = volume × density = (4/3) π R³ × ρ

Hence , acceleration due to gravity g = G [  (4/3) π R³ × ρ ] / R² = ( G (4/3) π  ρ ) R

Hence , acceleration due to gravity of earth is directly proportional to radius of earth .

Hence if radius decreases by 1% , then acceleration due to gravity is also decreases by 1 %