Question

A wall of length $\iota$ support water to a height H as shown in figure Choose the correct statement(s) Take $\rho$ as the density of water

• A. the force exerted by water on the wall per unit length is $\frac{1}{2}\rho g{H}^2$
• B. the force exerted by water on the wall is $\frac{1}{2}\rho g{H}^2\iota$
• C. the point of application of the resultant force acts $\frac{2}{3}H$ below the free surface
• D. the point of application of the resultant force acts $\frac{H}{3}$ below the free surface

Answer 1

Answer: (A), (B), (C)

The correct options are
A the force exerted by water on the wall per unit length is $\frac{1}{2}\rho g{H}^2$
B the force exerted by water on the wall is $\frac{1}{2}\rho g{H}^2\iota$
C the point of application of the resultant force acts $\frac{2}{3}H$ below the free surface

The pressure at the base of the dam is $\rho gh$

The force per unit length of the damis equal to the area of the pressure diagram $\frac{F}{\iota }=\frac{1}{2}\left(\rho gH\right)H=\frac{1}{2}\rho g{H}^2$

or F = $\frac{1}{2}\rho g{H}^2\iota$

The point of allication of the resultant force passes through the centroid of the pressure diagram i.e. at $\frac{H}{3}$ from the base or $\frac{2}{3}H$ from the top