Question

A cane filled with water is revolved in a vertical circle of radius $4$ metre and the water just does not fall down. The time period of revolution will be:

• A. $1$ sec
• B. $10$ sec
• C. $8$ sec
• D. $4$ sec

Answer 1

Answer: (D)

$4$ sec

at the topmost position

three forces will act on the water

1. weight in the downward direction
2. the normal reaction by a bucket in the downward direction
3. centrifugal force in the upward direction

From, the force balance

so $mg+N=\frac{m{v}^2}{r}$

for water just does not fall $N\ge 0$

so $mg=\frac{m{v}^2}{r}$

$v=\sqrt{gr}$

so time period T = $\frac{2\pi r}{v}$

=$\frac{2\times 3.14\times 4}{\sqrt{4g}}$

=$\frac{3.14\times 4}{\sqrt{9.8}}$

=4.01