Question

A cylindrical vessel of $90cm$ height is kept filled up to the brim. It has four holes $1,2,3$ and $4$ which are, respectively, at heights of $20cm,30cm,40cm$ and $50cm$ from the horizontal floor $PQ$. The water falling at the maximum horizontal distance from the vessel comes from:

• A. hole number $4$
• B. hole number $3$
• C. hole number $2$
• D. hole number $1$

Answer 1

Answer: (A), (B)

The correct options are
A hole number $4$
B hole number $3$

The maximum horizontal distance from the vessel comes from hole numbers 3 and 4. Now, $v=\sqrt{2gh}$, where $h$ is the height of the hole from the top.

Let say height of vessel is '$H$'.
The vertical distance travelled by the water is given as $H-h=\frac{1}{2}g{t}^2$
We get the time of descent as $t=\sqrt{\frac{2(H-h)}{g}}$
Horizontal distance,
$x=vt=\sqrt{2gh}\sqrt{\frac{2(H-h)}{g}}=2\sqrt{h(H-h)}$
Substituting the values we get the maximum distance for hole number 3 and 4.