Question

A bucket full of water is revolved in a vertical circle of radius $2m$. What should be the maximum time-period of revolution, so that the water doesn't fall out of bucket?

• A. $1sec$
• B. $2sec$
• C. $3sec$
• D. $4sec$

Answer 1

The correct option is C $3sec$

Let its angular velocity be $\omega$ at all points (uniform motion). At the highest point, weight of the body is balanced by centrifugal force, so
$m{\omega }^{2}r=mg\Rightarrow \omega =\sqrt{\frac{g}{r}}$
$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{r}{g}}=2\pi \sqrt{\frac{2}{10}}=\frac{2\pi }{\sqrt{5}}$

$T=\frac{2\times 3.14}{2.1}=3sec$