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 ) /(3) `
B. ` (rho g ) /(2 ) `
C. `(rho g ) /(6 ) `
D. ` (rho g )/(8) `

Answer

C

Explanation

Force on elemental strip at depth x due to water
` d F = rho gx xx 1 dx , (tau _ (CM) = F xx (1)/(2) + int d tau _ (w ) `
` tau _ (CM) = F xx (1)/(2) + int _ 0 ^ 1 rho gx dx ((1)/(2) - x ) , tau _ (CM ) = 0 , ` Hence ` F = (( rho g )/( 6 )) `