A body is moving in a vertical circle of radius ‘r’ by a string. If the ratio of maximum to minimum speed is 3:1, the ratio of maximum to minimum tensions in the string is___

VmaxVmin=n+4n=31 n+4n=31 n+4=3n⇒2n=4⇒n=2 TmaxTmin=n+5n−1=2+52−1=71

A body is moving in a vertical circle of radius ‘r’ by a string. If the ratio of maximum to minimum speed is 3:1, the ratio of maximum to minimum tensions in the string is___

VmaxVmin=n+4n=31 n+4n=31 n+4=3n⇒2n=4⇒n=2 TmaxTmin=n+5n−1=2+52−1=71

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A body is moving in a vertical circle of radius ‘r’ by a string. If the ratio of maximum to minimum speed is $\sqrt{3} : 1,$ the ratio of maximum to minimum tensions in the string is___

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3:1

5:1

7:1

9:1

answer is C.

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$\frac{V_{\max}}{V_{\min}} = \sqrt{\frac{n + 4}{n}} = \frac{\sqrt{3}}{1}$
$\frac{n + 4}{n} = \frac{3}{1}$
$n + 4 = 3 n \Rightarrow 2 n = 4 \Rightarrow n = 2$
$\frac{T_{\max}}{T_{\min}} = \frac{n + 5}{n - 1} = \frac{2 + 5}{2 - 1} = \frac{7}{1}$

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A body is moving in a vertical circle of radius ‘r’ by a string. If the ratio of maximum to minimum speed is 3:1, the ratio of maximum to minimum tensions in the string is___

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A body is moving in a vertical circle of radius ‘r’ by a string. If the ratio of maximum to minimum speed is $\sqrt{3} : 1,$ the ratio of maximum to minimum tensions in the string is___