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A small bob tied at one end of a thin string of length 1m is describing a vertical circle so that maximum and minimum tension in the string are in the ratio 5:1. The velocity of the bob at the highest position is ____m/s $(Take g = 10 m / s^{2})$

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answer is 5.

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Detailed Solution

Maximum tension is at lowest position and minimum tension is at the highest position.

Let the speed of bob at lowest position be v₁ and at the highest position be v₂ .

$T_{max} = mg + \frac{{mv}_{1}^{2}}{R}$

$T_{min} = \frac{{mv}_{2}^{2}}{R} - mg$

$\frac{T_{max}}{T_{min}} = \frac{5}{1}$

$\frac{1}{2} {mv}_{1}^{2} = \frac{1}{2} m {v_{2}}^{2} + 2 mgR$

$\Rightarrow v_{2} = 5 m / s$

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