If the radius of the earth decreases by $10\%$ while keeping the mass constant then the acceleration due to gravity will ________

We know that the acceleration due to gravity is given by:
$g= \frac{GM}{R^2}$
When the  mass is constant,
$\text{g}\propto {\text{R}}^{-2}$ 

$\frac{g_2}{g_1}={\left(\frac{{\text{R}}_{\text{1}}}{{\text{R}}_{\text{2}}}\right)}^2$

Since the radius is decreased by 10%, the new radius can be given as:
$R_2=\frac{90}{100}{R}_1$
$\frac{R_2}{R_1}=\frac{90}{100}$

$\frac{g_2}{g_1}={\left(\frac{100}{90}\right)}^2={\left(\frac{10}{9}\right)}^2=\frac{100}{81}$

$change in g=\frac{{\text{g}}_{\text{2}}-{\text{g}}_1}{{\text{g}}_{\text{1}}}=\frac{100}{81}-1=\frac{19}{81}$

$\% change in g=\frac{19}{81}\times 100=23.45\%$

Since the sign is positive, we can say that there is an increase in the percent change.
Hence the option D is the correct answer.