A cone filled with water is revolved in a vertical circle of radius...

A cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

Options

A2 s
B4 s
C1 s
D6 s

Correct answer

B. 4 s

Step-by-step solution

When a cone filled with water is revolved in a vertical circle, then the velocity at the highest point is given by Also

\begin{aligned} & v \geq \sqrt{g r} \\ & v=r w=r \frac{2 \pi}{T} \end{aligned}

Hence,

\quad \frac{2 r \pi}{T} \geq \sqrt{r g}

\begin{aligned} T & \leq \frac{2 \pi r}{\sqrt{r g}}=2 \pi \sqrt{\frac{r}{g}}=2 \pi \sqrt{\frac{4}{9.8}} \\ & =2 \times 3.14 \times 0.6389=4.0 \mathrm{sec} \end{aligned}

So,

T_{\max }=4 \mathrm{sec}$

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