Question

At the mouth of the tap, the area of cross-section is $2.0c{m}^2$ and the speed of water is $3m/s$. The area of cross-section of the water column $80cm$ below the tap is(use $g=10m/s^2$):

• A. $0.6c{m}^2$
• B. $1.2c{m}^2$
• C. $1.5c{m}^2$
• D. $2.0c{m}^2$

Answer 1

Answer: (B)

$1.2c{m}^2$

Velocity of water $80$ cm below the top be $V$,
$V^2=U^2+2as$
$\Rightarrow V^2=9+2\times 10\times \frac{8}{10}$
$V^2=25\Rightarrow V=5m/s$
So,
From equation of Continuity,
$A_1{V}_1=A_2{V}_2$
$\Rightarrow 2\times 3=5\times A_2$
$\Rightarrow A_2=\frac{6}{5}c{m}^2\Rightarrow A_2=1.2c{m}^2$