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Question

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
119570.png

A
4aghρR
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B
8aghρR
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C
2aghρR
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D
none of these
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Solution

The correct option is A 4aghρR
Velocity of efflux of water v=2g(h2)=gh
Force on ejected water = Rate of change of momentum of ejected water
F=ρav2
Torque of these forces about central line =(ρav2)×(4R)
=4ρav2R=4ρaghR
158949_119570_ans.png

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