Question

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

• A. 2 s
• B. 4 s
• C. 8 s
• D. 10 s

Answer 1

Answer: (B)

4 s

Answer 2

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