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 ( ρ is the density of water):

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 ( ρ is the density of water): (A) (h2 b ρ g/2) (B) (h2 b2 ρ g/4) (C)  2 hbρ g  (D) (h2 b ρ g/4)

Tardigrade Admin · Accepted Answer

Here: Height of water level =h Width of dam =b, density of water =ρ The force is given by, F= pressure × area or F=(h ρ g/2) × h b Hence, F=(h2 b ρ g/2)

Q. 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 ( $ρ$ is the density of water):

$\frac{h ^{2} b ρ g}{2}$

$\frac{h ^{2} b ^{2} ρ g}{4}$

$2 hb ρ g$

$\frac{h ^{2} b ρ g}{4}$

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

Q. 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 ( ρ is the density of water):

2h2bρg​

4h2b2ρg​

2hbρg

4h2bρg​