If the radius of the earth were to shrink by 2% its mass remaining the same, by how much percentage would the acceleration due to gravity on the earth's surface would increase?

$\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{R}}^2}$ (if R increases, g decreases)

Taking logarithms on both the sides, we get

$\log \mathrm{g}=\log \mathrm{G}+\log \mathrm{M}-2\log \mathrm{R}$

Differentiating, we get $\frac{\mathrm{dg}}{\mathrm{g}}=0+0-\frac{2\mathrm{dR}}{\mathrm{R}}$

$\frac{\mathrm{dg}}{\mathrm{g}}=-2\left(\frac{-2}{100}\right)=\frac{4}{100}$

$\%\text{ increase in }g=\frac{dg}{g}\times 100=\frac{4}{100}\times 100=4\%$