If the radius of earth shrinks by 2 % while its mass remains same. The acceleration due to gravity on the earth's surface will approximately

Step-by-step solution

The acceleration due to gravity on the surface of the earth is given by, g = G M R 2 . The radius shrunk by 2 % . Therefore, ∆ R R × 100 = - 2 % . As the mass is constant and the change in the radius of the earth is relatively small, we can write ∆ g g = - 2 ∆ R R ⇒ ∆ g g × 100 = 4 % Hence, the acceleration due to gravity increases by 4 % .