Question

A can filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. The maximum possible time period for a revolution is about :

• A. $2s$
• B. $4s$
• C. $8s$
• D. $10s$

Answer 1

The correct option is B $4s$

When a body is revolving in circular motion, it is acted upon by a centripetal force directed towards the centre. Water will not fall, if weight is balanced by centripetal force. Therefore,
$mg=\frac{m{v}^2}{r}$
$\Rightarrow v^2=rg\Rightarrow v=\sqrt{rg}$ .....(i)
Circumference of a circle is $2\pi r$
Time for a revolution $=\frac{2\pi r}{v}$
On putting the value of v from Eq. (i), we get
$T=\frac{2\pi r}{\sqrt{gr}}=2\pi \sqrt{\frac{r}{g}}$
Given, $r=4m,g=9.8m{s}^{-2}$
$\therefore T=2\pi \sqrt{\frac{4}{9.8}}$
$\Rightarrow T=\frac{4\pi }{\sqrt{9.8}}=4s$