Suppose the radius of earth is shrunk by 1% with constant mass. What would happen to the acceleration due to gravity on the surface of earth?

The acceleration due to gravity on the surface of earth is, $g=\frac{GM}{R^2}\;\;\text{__(1)}$

Differentiating both sides, we get, $dg=-\frac{2GM}{R^3}dR\;\;\text{__(2)}$

Dividing equation $(2)$ by $(1)$, we get, $\frac{dg}{g}=-\frac{2dR}{R}$

Percentage change in $g$ is, $\frac{dg}{g}×100\%=-2\left(\frac{dR}{R}×100\%\right)$

The radius of earth is shrunk by $1\%$, $\therefore\frac{dR}{R}×100\%=-1\%$

Now, $\frac{dR}{R}×100\%=(-2)(-1\%)=2\%$

Hence, the acceleration due to gravity on the surface of earth will increase by 2%.