Question

An open cylinderical tank of height $2m$ and radius $\sqrt{5}m$ contains water up to a height of $1.5m$. The maximum frequency of rotation attained by the tank without spilling any water is

• A. 19 rpm
• B. 17 rpm
• C. 22 rpm
• D. 18 rpm

Answer 1

The correct option is A 19 rpm

Step 1: Draw rough figure for given situation.



Step 2: Find the value of $y$.
Given , height of the tank, $H=2m$
Height of water in the tank , $h=1.5m$
If the water doesnot come out of the tank, it can rise maximum $H-h=0.5m$
$\text{Maximum rise = maximum fall=0.5m}$
$y=2[2-1.5]=1m$
Step 3: Find maximum frequency of rotation.
formula $y=\frac{{\omega }^2{r}^2}{2g}$
Given , radius of the tank $r=\sqrt{5}m$
As we know $y=\frac{{\omega }^2{r}^2}{2g}$
$\Rightarrow 1=\frac{{\omega }^2(\sqrt{5}{)}^2}{2\times 10}$
$\Rightarrow \omega =2rad/s$
$f=\frac{\omega \times 60}{2\pi }rpm$
$f=\frac{2\times 60}{2\pi }=19rpm$

Final answer: (c)