First slide

Vertical circular motion

Question

A body tied with string of length l and rotates in a vertical circle. If the maximum tension is two times the minimum tension then the minimum speed of the body is __

Moderate

A

$\sqrt{7 g l}$
B

$\sqrt{5 g l}$
C

$\sqrt{3 g l}$
D

$\sqrt{6 g l}$

Solution

$\begin{array}{l} T_{\max} = 2 T_{\min} \\ T_{\max} - T_{\min} = 6 m g \\ 2 T_{\min} - T_{\min} = 6 m g \\ T_{\min} = 6 m g \\ \frac{m v^{2}}{l} - m g = 6 m g \\ \frac{m v^{2}}{l} = 7 m g \\ V = \sqrt{7 g l} \end{array}$

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