Question

A ball of density $\sigma$ is released from rest from the centre of an accelerating sealed cubical vessel completely filled with a liquid of density $\rho$. If the trough moves with a horizontal acceleration ${\overrightarrow{a}}_0$, find the initial acceleration of the ball

Answer 1

So net acceleration = $\frac{F_{net}}{massofball}$

$F_{net}=\sqrt{{\left(\sigma V\overrightarrow{a_0}\right)}^2+{(\sigma -\rho )}^2{V}^2{g}^2}$

mass of ball = $\sigma V$

So, $a_{net}=\frac{\sqrt{{\sigma }^2{a}_0^2+{(\sigma -\rho )}^2{g}^2}}{\sigma }$

$a_{net}=\sqrt{a_0^2+{(1-\frac{\rho }{\sigma })}^2{g}^2}$