First slide

Vertical circular motion

Question

A small block of mass m is attached to one end of a string OA of length l as shown in figure. The end O of the string is fixed at point O and the block is released with the string horizontal. If $m = 2 k g$ , find the maximum tension induced in the string. Take $g = 10 m / s^{2}$ .

Easy

A

80 N
B

100 N
C

40 N
D

60 N

Solution

Tension in the string is maximum when the string will be vertical. At this instant, conserving energy, $\frac{1}{2} m V^{2} = m g l \Rightarrow \frac{m V^{2}}{l} = 2 m g$
$∴ T_{\max} = m g + \frac{m V^{2}}{l} = m g + 2 m g = 3 \times 2 \times 10 N = 60 N$

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