Question

Water and mercury are filled in two identical cylindrical vessels up to the same height. Both vessels have a tiny hole in the wall at the bottom. The velocity of water and mercury coming out of the holes are $v_1$ and $v_2$ respectively. Then:
[Density of mercury $=13.6\text{g/cc}$]

• A. $v_1=v_2$
• B. $v_1=13.6v_2$
• C. $v_1=\frac{v_2}{13.6}$
• D. $v_1=\sqrt{13.6}{v}_2$

Answer 1

The correct option is A $v_1=v_2$

We know that for small height of vessel, speed of efflux is given by, $v=\sqrt{2gh}$.
This speed is independent of nature of fluid i.e. independent of density.
Hence, speed of water and mercury coming out of the holes will be equal as height is the same
$\therefore v_1=v_2$