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) \[2\,\,s\]                                             

B) \[4\,\,s\]

C) \[8\,\,s\]                                             

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\[=\frac{2\pi r}{r}\] Putting the value of v from Eq. (i), we get                 \[T=\frac{2\pi r}{\sqrt{gr}}=2\pi \sqrt{\frac{r}{g}}\] Given,\[r=4\,\,m,\,\,g=9.8\,\,m/{{s}^{2}}\] \[\therefore \]  \[T=2\pi \sqrt{\frac{4}{9.8}}=T=\frac{4\pi }{\sqrt{9.8}}=4s\]