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A square gate of size 1mxx1m is hinged a...

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

A

` ( rho g ) /(3) `

B

` (rho g ) /(2 ) `

C

`(rho g ) /(6 ) `

D

` (rho g )/(8) `

Text Solution

Verified by Experts

The correct Answer is:
C
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 )) `
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