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The fig shows a semo-cylinderical massle...


The fig shows a semo-cylinderical massless gate of unit length perpendicular to the plane of the page and is pivoted at the point `O` holding a stationary liquid of density `rho`. A horizontal foce `F` is applied at its lowest position to keep it stationary. The magnitude of the force is:

A

`(3)/(2)rhogR^(2)`

B

`(9)/(2)rhogR^(2)`

C

`rhogR^(2)`

D

`2rhogR^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Torque about `O` due to water pressure is given
by `tau=int d tau`
When `dtau=dF.Rsintheta` after intergrating from 0 to `180^(@)` we will get `tau=4R^(3)rhog`
this should be balanced by applied torque.
`becausetau=4R^(3)rhog=F(2R)`
`impliesF=2rhogR^(2)`
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