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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

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 4aghρRAs we know, →τ=→r×→F-----(1) Where, r=distance between two limbs i.e. 4R F=d(mv)dt=mdvdt+vdmdt F=vdmdt (∵ velocity is constant) F=v×ρ×a×v (∵dmdt=ρav) F=ρav2 τ=4R×ρav2 v=√2gH From diagram we get H=h2 so, v2=2gh2=gh put v2 in equation (1) τ=4Rρagh

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