A square gate of size `1mxx1m` is hinged at its mid point. A fluid of density `rho` fill the space to the left of the gate. The force `F` required to hold the gate stationary is

Options

A. `(rho g)/(6)`
B. `(1)/(2)rho g`
C. `(rho g)/(6)`
D. None of these

Answer

C

Explanation

Net torque about hinge =0
`dF=(rho gh)(1*dx)`
`dtau =(rho gh)(x-0.5)dx`
`:.` Net anticlockwise torque
`int _(0)^(1)d tau=((rho g)/(12))`
Net clockwise torque of applied force `=F(0.5)=(F)/(2)`.
Equanting the two torques we get,
`F=(rho g)/(6)`.