Answer
$6.5\;mm$
Work Step by Step
According to Archimedes’ principle the buoyant force is equal to the alligator’s weight
$F_b=W\;........................(1)$
or, $\rho_w gAh=mg$
or, $\rho_w Ah=m$
Let, the alligator would sink additional $\Delta h$ after swallowing stones
Now, the Eq. $(1)$ becomes,
$\rho_w g A(h+\Delta h)=(m+\Delta m)g$
or, $\rho_w A\Delta h=\Delta m$
or, $\Delta h=\frac{\Delta m}{\rho_w A}$
Substituting the given values
$\Delta h=\frac{0.01\times130}{1000\times0.20}$
or, $\Delta h=6.5\times10^{-3}\;m$
or, $\boxed{\Delta h=6.5\;mm}$
