If the radius of earth shrinks by 2 % while its mass remains same. The acceleration due to gravity on the…

The acceleration due to gravity on the surface of the earth is given by, $g=\frac{GM}{R^2}$.

The radius shrunk by $2\%$. Therefore, $\frac{∆R}{R}\times 100=-2\%$.

As the mass is constant and the change in the radius of the earth is relatively small, we can write

$$\begin{gathered} \frac{∆g}{g}=-2\frac{∆R}{R} \\ \Rightarrow \frac{{\displaystyle ∆g}}{{\displaystyle g}}\times 100=4\% \end{gathered}$$

Hence, the acceleration due to gravity increases by $4\%$.