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  • A ring of mass 'm' and radius 'r' is gently placed on a conveyer belt moving with a uniform velocity 'v'. If the coefficient between the belt and the ring is 'u' the

A ring of mass 'm' and radius 'r' is gently placed on a conveyer belt moving with a uniform velocity 'v'. If the coefficient between the belt and the ring is 'u' then find the time after which it starts pure rolling.

Option: 1

\frac{v}{2\mu g}


Option: 2

\frac{\mu g}{2v}


Option: 3

\frac{v}{\mu g}


Option: 4

\frac{\mu g}{v}


Answers (1)

best_answer

\mu N=ma

Taking torque about the COM.

\tau=rf=\mu Nr\\ a=\mu g\\

After time 't' it starts rolling.

v^{'}+w^{'}r=v\\ \mu gt +\frac{\mu gt}{r}\times r=v\\ 2\mu gt=v\\ t=\frac{v}{2\mu g}

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