If the radius of the earth were to shrink by 1 % its mass remaining same, the acceleration due to gravity on the earth's surface would

Step-by-step solution

g = G M R 2 ;   g ′ = G M R ′ 2 = G M 100 2 99 2 R 2 % increase in g = ( g ′ - g ) × 100 g = g ′ g - 1 × 100 = 100 99 2 - 1 × 100 1 + 1 99 2 - 1 × 100 ≈ 2 %