Correct choice is (d) 9622
Easy explanation: To keep the gate closed, moment due to weight of the gate should be balanced by the moment due to the hydrostatic force.
where m = mass of the plate, θ = angle of inclination to the horizontal, Fhyd = hydrostatic force on
the plate, x = distance of the point of action of Fhyd from the hinge point = ^2⁄3 * 5 = ^10⁄3
Fhyd = γyA, where γ = specific weight of the liquid = 9.81 * 10^3 y = depth of the centre of pressure from the free surface = 2.5/2 = 1.25 and A = 5 * 1. Substituting all the values in the equation, we get m = 9622.5g.