JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Fluid Mechanics

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The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth '

h

' below the water level. The value of '

h

' for which the emerging stream of water strikes the ground at the maximum range is ____ m.

Answer: 6

Solution

Torricelli's law gives the horizontal efflux speed at depth

h

v = 2 g h

. The jet then falls the remaining height

H - h

as a projectile, taking

t = \frac{2 ( H - h )}{g}

so the range on the ground is

R = v t = 2 g h \frac{2 ( H - h )}{g} = 2 h (H - h)

The product

h (H - h)

is largest when

h = \frac{H}{2}

. With

H = 12

m, the range is maximum for a hole at a depth of

6

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Numerical answer

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