Water is filled up to a height h in a beaker | vedclass

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(B) The force on one side of the section $ABCD$ is due to the pressure of the water and the surface tension at the free surface.The pressure at a dept

Vedclass · Accepted Answer

$| 2P_0Rh + R\rho gh^2 - 2RT |$

Vedclass · Answer

(B) The force on one side of the section $ABCD$ is due to the pressure of the water and the surface tension at the free surface.The pressure at a depth $y$ from the surface is $P(y) = P_0 + ho gy$.The area of the vertical section $ABCD$ is $A = (2R) 	imes h = 2Rh$.The force due to pressure is the integral of $P(y) dA$ over the section:$F_p = \int_0^h (P_0 + ho gy) (2R) dy = 2R [P_0 y + \frac{1}{2} ho g y^2]_0^h = 2R (P_0 h + \frac{1}{2} ho g h^2) = 2P_0 Rh + R ho g h^2$.The surface tension $T$ acts along the length of the free surface of the section,which is the diameter of the beaker,$2R$. The force due to surface tension is $F_T = T 	imes (2R) = 2RT$.The net force on one side of the section is the difference between the pressure force and the surface tension force:$F_{net} = |F_p - F_T| = |2P_0 Rh + R ho g h^2 - 2RT|$.

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