Question

A cane 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?

• A. 2 s
• B. 4 s
• C. 1 s
• D. 6 s

Answer 1

Answer: (B)

4 s

Answer 2

When a cane filled with water is revolved in a vertical circle, then the velocity at the highest point is given by $v\ge \sqrt{g\,r}$ Also $v=r \omega=r \cdot \frac{2 \pi}{T}$ Hence, $d \frac{2 \pi r}{T} \geq \sqrt{r g}$ $T \leq \frac{2 \pi r}{\sqrt{r g}}=2 \pi \sqrt{\frac{r}{g}}$ $\leq 2 \pi \sqrt{\frac{4}{9.8}}$ $\leq 2 \times 3.14 \times 0.638$ $\leq 4.0\, s$ $T_{\max }=4\, s$