Question

The cross-sectional area of a large tank is $0.5m^2$. It has an opening near the bottom having cross-sectional area $1c{m}^2$. A load of $20kg$ is applied on the water at the top. The velocity of water coming out of the opening, at the time when the height of water level is $50cm$ above the bottom is nearly:(Take $g=10m{s}^{-2}$)

• A. $1.15$
• B. $3.15$
• C. $5.15$
• D. $715$

Answer 1

Answer: (B)

$3.15$

Applying Bernoullis theorem across the two points.
$\frac{2000}{0.5}+1000\times 10\times \frac{50}{100}=\frac{1}{2}\times 1000\times v^2$

$\Rightarrow 400+5000=500v^2$

$\Rightarrow \frac{54}{5}=v^2\Rightarrow v=3.286m/s$

$\Rightarrow v\approx 3.3m/s$ .....[ Neglecting the velocity of water at the top of beaker ]