Question

If radius of earth shrinks by 1% then for acceleration due to gravity :

Answer 1

The acceleration due to gravity g = GM/r2 = 9.8 m/s2 If r reduces by 1%, the new radius becomes r' = 99% of r = 99r/100 = 0.99r New acceleration due to gravity g' = GM/(0.99r)2 = GM/(0.98r2 ) = 1.04 g = 10.19 m/s2 Increase in acceleration due to gravity = 10.19 − 9.8 m/s2 = 0.39 m/s2 Increase in percentage = 0.39 x 100/9.8 = 3. 97%