question_answer

A can filled 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)  2s             

B)  4s

C)  8s              

D)  10 s

Correct Answer: B

Solution :

 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, \[mg=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \] \[{{v}^{2}}=rg\] ?(i) Circumference of a circle is \[2\pi r.\] Time for a revolution\[=\frac{2\pi r}{v}\] Putting the value of \[v\] from Eq. (i), we get \[T=\frac{2\pi r}{\sqrt{gr}}=2\pi \sqrt{\frac{r}{g}}\] Given, \[r=4m,g=9.8\,m/{{s}^{2}}\] \[\therefore \] \[T=2\pi \sqrt{\frac{4}{9.8}}T=\frac{4\pi }{\sqrt{9.8}}=4s\]