Question

If the radius of earth shrinks by 2%,mass remaining constant.How would the value of acceleration due to gravity change

Answer 1

The acceleration due to gravity at the surface of earth is g = G m / R2  .

The radius of earth 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 %