Question

The figure shows a light container kept on a horizontal rough surface of coefficient of friction $\mu =\frac{sh}{v}$. A very small hole of area s is made at a depth h. Water of volume V is filled in the container. The friction is not sufficient to keep the container at rest. The initial acceleration of the container is,

• A. $\frac{Vg}{Sh}$
• B. g
• C. zero
• D. $\frac{Shg}{v}$

Answer 1

The correct option is D $\frac{Shg}{v}$

$V_{efflux}=\sqrt{2gh}$
Force exerted by the liquid on the container =$\rho s(\sqrt{2gh}{)}^2$
Acceleration of the container, $a=\frac{2\rho Sgh-\mu \rho vg}{\rho v}$
$=(\frac{2Sh}{v}-\mu )g$

$=(\frac{2Sh}{v}-\frac{Sh}{v})g$

$=\frac{Shg}{v}$