First slide

Vertical circular motion

Question

The maximum and minimum tensions in the string used to rotate a body in a vertical circle are in the ratio 19:1. The ratio of maximum to minimum speeds of the body

Difficult

A

2:1
B

19:1
C

4;14
D

5:1

Solution

$we know T_{\max} - T_{\min} = 6 mg given \frac{T_{\max}}{T_{\min}} = 19 T_{\max} = 19 T_{\min} substituting 18 T_{\min} = 6 mg T_{\min} = \frac{mg}{3} \frac{{mv}_{2}^{2}}{l} - mg = \frac{mg}{3}; \frac{{mv}_{2}^{2}}{l} = \frac{4 mg}{3} \Rightarrow (1) then T_{\max} = 19 \frac{mg}{3} = \frac{{mv}_{1}^{2}}{l} + mg \frac{{mv}_{1}^{2}}{l} = 16 \frac{mg}{3} \Rightarrow (2) dividing (2) by (1) \frac{v_{1}}{v_{2}} = \frac{2}{1}$

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