Question

A container filled with liquid up to height $h$ is placed on a smooth horizontal surface. The container is having a small hole at the bottom. As the liquid comes out from the hole, the container moves in a backward direction with acceleration $a$ and finally, when al liquid is drained out, it acquires a velocity $v$. Neglect mass of the container. In this case

• A. both $a$ and $v$ depend on $h$
• B. only $a$ depends on $h$
• C. only $v$ depends on $h$
• D. neither $a$ nor $v$ depends on $h$

Answer 1

The correct option is D neither $a$ nor $v$ depends on $h$

$V=\sqrt{2gh}\Rightarrow$ V depends on 'h'

$a=\frac{dV}{dt}=\sqrt{2g}\times \frac{1}{2\sqrt{h}}\frac{dh}{dt}=\sqrt{\frac{g.g}{2hg}}V=\frac{gV}{2V}=\frac{g}{2}a=\frac{g}{2}\Rightarrow a$

is independent of h