If the radius of the earth suddenly decreases to 80% of its present value, the mass of the earth remaining the same, the value of the acceleration due to gravity will

Now $g=\frac{GM}{R^2}$. If R reduces to $R^{\text{'}}=0.8R$, the value of g becomes
$$\begin{gathered} g^{\text{'}}=\frac{GM}{R^{\text{'}2}}=\frac{GM}{0.64R^2} \\ =\frac{g}{0.64}=\frac{9.8{ \mathrm{ms}}^{-2}}{0.64} \end{gathered}$$
Increase in value of $g=\frac{g}{0.64}-g=\frac{0.36g}{0.64}$
Percentage increase $=\frac{0.36 \mathrm{g}}{0.64 \mathrm{g}}\times 100=56.25\%$
Hence the correct choice is (4).