Question

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

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

Answer 1

Answer: (D)

$4sec$

For the water not to fall down, the weight of the water must be balanced by the centrifugal force.
$mg=m\frac{v_{min}^2}{r}$
$v_{min}=\sqrt{gr}$

For $1$ revolution,
$v=\frac{2\pi r}{T}$
$\therefore T=\frac{2\pi r}{v}$
$\therefore T=\frac{2\pi r}{\sqrt{gr}}$
$\therefore T=2\pi \sqrt{\frac{r}{g}}$
$\therefore T=\frac{4\pi }{\sqrt{g}}$

$⟹T=4.01sec$