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Figure shows a semi-cylindrical massless...

Figure shows a semi-cylindrical massless gate pivoted at the point `O` holding a stationary liquid of density `rho`. The length of the cylinder is `l`. Calculate, the horizontal force exerted by the liquid on the gate.

A

`4rhogR^(2)l`

B

`rhogR^(2)l`

C

`4rhogR^(3)l`

D

none

Text Solution

Verified by Experts

The correct Answer is:
A
The force exerted by liquid on the gate is
`f_(H)=P_(av)xx`vertical projection area of the gate
`=((P_(A)-P_(B))/2)xx(2Rl)`
`=((Rrhog+3Rrhog)/2)xx2Rl=4rhogR^(2)l`
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