# The greatest and the least depth of a circular plate of 4 m diameter from the free surface of water are 3m and 1 m respectively as shown. What will be the depth (in m) of it’s centre of pressure?

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The greatest and the least depth of a circular plate of 4 m diameter from the free surface of water are 3m and 1 m respectively as shown. What will be the depth (in m) of it’s centre of pressure?

(a) 1.125

(b) 1.25

(c) 2.125

(d) 2.25

I'd like to ask this question from Hydrostatic Force on Plane Area in section Hydrostatic Forces on Surfaces of Fluid Mechanics

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The correct option is (c) 2.125

Explanation: The depth of the centroid y and the centre of pressure yCP are related by:

where I= the moment of inertia and A = area and θ = the angle of inclination of the lamina to the horizontal. Now,

y = 1 + 3 – 1 / 2 = 2, I = ^π ⁄ 64 * 4^2 = 4π,  A = ^π ⁄ 4 * 4^2 = 4π, sin θ = ^1 ⁄ 2 Thus, yCP = 2.125m.

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