Question

A container having a hole at the bottom is free to move on a horizontal
surface. As the liquid comes out, the container moves in a backward direction
with an acceleration $\alpha$ and finally acquires a velocity v (when all the liquid has drained out). Neglect the mass of the container. The correct option
out of the following is :

• A. Only v depends on h
• B. Only $\alpha$ depends on h
• C. Both v and $\alpha$ depend on h
• D. Neither v nor $\alpha$ depends on h .

Answer 1

The correct option is C Both v and $\alpha$ depend on h

The velocity through the hole of the body will be $v=\sqrt{(2\times g\times h)}$ as per the laws of fluid mechanics.

Since the container is initially at rest, its initial velocity=u=0.

Due to momentum conservation, the container will have some final velocity V.

This means that it has accelerated from 0m/s to V m/s.

Therefore, the acceleration must also depend on the height h. Hence, the answer is option c.