Question

Water stands upto a height $h$ behind the vertical wall of a dam. If width of the dam be $b$, then the net horizontal force pushing the dam down by the stream will be ( $\rho$ is the density of water):

• A. $\frac{h^{2} b \rho g}{2}$
• B. $\frac{h^{2} b^{2} \rho g}{4}$
• C. $ 2\,hb\rho g $
• D. $\frac{h^{2} b \rho g}{4}$

Answer 1

Answer: (A)

Here: Height of water level $=h$
Width of dam $=b$, density of water $=\rho$
The force is given by,
$F=$ pressure $\times$ area
or $F=\frac{h \rho g}{2} \times h b$
Hence, $F=\frac{h^{2} b \rho g}{2}$