The radius of earth is reduced by 4%. the mass of earth remains

CBSE Class 11
1

The radius of earth is reduced by 4%. the mass of earth remains unchanged. what will be the change in escape velocity???

2

The acceleration due to gravity at the surface of earth is g = Gm /R2.
The radius of eath decreases by 4 %, therefore
R’ = R - 0.04 R = 0.96R.
Now acceleration due to gravity will be :
g’ = GM / ( 0.96 R )2 = 1.09 g
Percentage increase in acceleration due to gravity
[(g’ - g )/g ] x 100 = 9 %