Question

if the radius of earth shrinks by 2% ,mass remaining constant,then how would the value of acceleration due to gravity change.
witn simple method

Answer 1

The acceleration due to gravity at the surface of earth is g = G m / R² .
The radius of eath decreases by 2 %, therefore
R' = R - 0.02 R = 0.98R.
Now acceleration due to gravity will be :
g' = GM / ( 0.98 R )2 = 1.04 g
Percentage increase in acceleration due to gravity
[(g' - g )/g ] x 100 = 4 %