A cylindrical container of radius 'R' and height 'h' is completely filled with a liquid. Two horizontal L-shaped pipes of small cross-sectional area 'a' are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is

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$4 aghρR$

$8 aghρR$

$2 aghρR$

none of these

answer is A.

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Detailed Solution

velocity of efflux of water $v = \sqrt{2 g (\frac{h}{2})} = \sqrt{gh}$

Force on ejected water = Rate of change of momentum of ejected water

$F = {ρav}^{2}$

Torque of these forces about central line $= ({ρav}^{2}) \times (4 R)$

$= 4 {ρav}^{2} R = 4 ρaghR$

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