A cylinder of height $h$ is filled with water and is kept on a block of height $h / 2$ . The level of water in the cylinder is kept constant. Four holes numbered $1, 2, 3$ and $4$ are at the side of the cylinder and at heights $0,\ h / 4,\ h / 2$ and $3h / 4$ respectively. When all four holes are opened together, the hole from which water will reach farthest distance on the plane $PQ$ is the hole number
Diffcult
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Suppose there is a hole in the cylinder at depth $y$ below water level Velocity of efflux $v=\sqrt{2 g y}$

Time taken by water to reach on the plane $PQ$ will be

$t=\sqrt{\frac{2\left(\frac{h}{2}+(h-y)\right)}{g}}-\sqrt{\frac{3 h-2 y}{g}}$

Horizontal distance $x$ travelled by the liquid is $x=v t-\sqrt{2 g y} \sqrt{\frac{3 h-2 y}{g}}, \quad x=\sqrt{2 y(3 h-2 y)}$

For $x$ to be maximum, $\frac{d x}{d y}=0$

$\frac{1}{2 \sqrt{2 y(3 h-2 y)}} \times 2(3 h-4 y)=0$

Or           $3 h-4 y-0 ; \quad y=\frac{3 h}{4}$

Hence, $x$ will be maximum at $y=\frac{3 h}{4}=\left(h-\frac{h}{4}\right)$

Where, hole number $2$ is present.

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