# A cylinder of radius R is kept embedded along the wall of a dam as shown. Take density of water as rho. Take length as L. The force exerted by liquid on the cylinder in horizontal direction is [Neglecting atmospheric pressure]?

## A) $2 {R}^{2} \rho g L$ B) ${R}^{2} \rho g L$ C) $4 {R}^{2} \rho g L$ D) $1.61 {R}^{2} \rho g L$

Aug 28, 2017

Average horizontal pressure on the surface of cylinder

${P}_{\text{ave}} = \rho g {h}_{C}$
where ${h}_{C}$ is depth of centroid (midpoint) of the surface

Inserting value of ${h}_{C}$ from the figure

${P}_{\text{ave}} = \rho g \left(R + R\right) = 2 R \rho g$

Area of the cylinder exposed to pressure$= 2 R \times L$

Now $\text{Force"="Pressure"xx"Area}$

$\therefore \text{Force} = 2 R \rho g \times 2 R L = 4 {R}^{2} \rho g L$