First slide

Vertical circular motion

Question

A particle of mass 100 gm tied to a light string of length 40 cm and related along a vertical circular path. What should be the minimum speed at the highest point of its path so that the string does not become slack at any position?

Moderate

A

$2 \sqrt{2} m / s$
B

2 m/s
C

zero
D

$\sqrt{2} m / s$

Solution

For the minimum speed at the highest point, the string will be just taut i.e. tension will be just zero.
Therefore, $\frac{m V^{2}}{l} = m g \Rightarrow V = \sqrt{g l} = \sqrt{10 \times 0 .4} m / s = 2 m / s$

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