First slide

Vertical circular motion

Question

A can 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

Moderate

A

1 sec
B

10 sec
C

8 sec
D

4 sec

Solution

The speed at the highest point must be
$v \geq \sqrt{rg}$
Now $v = rω = r (2 π / T)$
$∴ r (2 π / T) \geq \sqrt{rg}$
or $T \leq \frac{2 πr}{\sqrt{rg}} \leq 2 π \sqrt{(\frac{r}{g})}$
$∴ T_{max} = 2 π \sqrt{(\frac{4}{9 \cdot 8})} = 4 \sec$

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