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Question

A square gate of size 1m×1m is hinged at its mid-point. A fluid of density ρ filled the space to the left of the gate. The force F required to hold the gate stationary is 

 


A
ρg3
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B
ρg2
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C
ρg6
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D
None
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Solution

The correct option is B ρg6
Net torque about hinge is zero
120ρg[x+12].xdx120ρg[12x]xdx=F.12ρg[x33+12x22]120ρg[x24x33]120=F2
On solving we get F=ρg6

Physics

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