A square gate of size `1mxx1m` is hinged at its midpoint. A fluid of denisty `rho` fills the space to the left of the gate. The force `F` required to hold the gate stationary is

Options

A. `(rhog)/3`
B. `(rhog)/2`
C. `(rhog)/6`
D. `(rhog)/8`

Answer

C

Explanation

At a depth `y` from tfhe surface of the fluid, the net force acting on the gate element of width `dy` is
`dF=(p_(0)+rhogy-p_(0))xx1dy=rhogydy`
Torque of this force about the hinge is
`dtau=rhogydyxx(1/2-y)`
Net torque experienced by the gate is
`tau_("net")=inttau+Fxx1/2`
`=int_(0)^(1)rhogydy(1/2-y)+Fxx1/2=0`
`impliesF=(rhog)/6`