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  4. A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is

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Q. A tank is filled up to a height $2\, H$ with a liquid and is placed on a platform of height $H$ from the ground. The distance $x$ from the ground where a small hole is punched to get the maximum range $R$ isPhysics Question Image

Mechanical Properties of Fluids

Solution:

As $x=\frac{1}{2} g t^{2} \Rightarrow t=\sqrt{\frac{2 x}{r}}$
Velocity of efflux $v=\sqrt{2 g(H-x)}$
Hence $R=v t=2 \sqrt{x(3 H-x)}$
For range to be maximum $\frac{d R}{d x}=0$
which gives $x=\frac{3}{2} H=1.5\, H$
Alternatively:
Maximum range is also equal to average of two heights
$x=\frac{H+2 H}{2}=\frac{3 H}{2}=1.5\, H$