Question

If the radius of the earth shrinks by 4% and there is no change in its mass, the value of g increases by ___ %.

Answer 1

$M_e$ and R are the mass and radius of the earth, $g_1$ and $g_2$ are the acceleration due to gravity before and after shrink respectively.
We know,
$g_1=\frac{G{M}_e}{R_1^2}$ & $g_2=\frac{G{M}_e}{R_2^2}$
Given,
$R_2=\left(\frac{96}{100}{R}_1\right)$
$\therefore \frac{g_2}{g_1}=\frac{GM}{{0.96}^2{R}^2}\times \frac{R^2}{GM}$
$=\frac{1}{0.96\times 0.96}=1.08$
$\therefore g_1$ increases by 8%