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)`

The fig shows a semo-cylinderical massless gate of unit length perpen

1.	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)`
Answer» Correct Answer - 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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