A particle is whirled in a vertical circle of radius 1.0 m using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$ , the minimum velocity of the particle is :
Take g = 10 m/s².

Question

A particle is whirled in a vertical circle of radius 1.0 m using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$ , the minimum velocity of the particle is :

Particle on string moving in a vertical circle

Take g = 10 m/s².

TestHub · Accepted Answer

Minimum speed and tension occur at the top. Let the top speed be v.

$v_{b}^{2} = v^{2} + 4 g R$

$T_{b} = m (\frac{v ^{2}}{R} + 5 g)$

$T_{t} = m (\frac{v ^{2}}{R} - g)$

$\frac{T _{b}}{T _{t}} = \frac{v ^{2} + 5 g R}{v ^{2} - g R} = \frac{5}{3}$

$v^{2} = 10 g R = 100 m^{2} / s^{2}$

$v = 10 m/s$

Option C.

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