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  • A thin circular ring of mass M and radius R is rotating with a constant angular velocity <img alt="2\: \: rads ^{-1}" src="https://entrancecorner.oncodecogs.com/gif.latex?2%5C%3A%20%5C%3A%20rads%20

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2\: \: rads ^{-1} in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass \mathrm{m} be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads^{-1}).
 

Option: 1

\begin{aligned} &\frac{M}{(M+m)}\\ \end{aligned}


Option: 2

\begin{aligned} &\frac{(M+2 m)}{2 M} \\ \end{aligned}


Option: 3

\frac{2 M}{(M+2 m)} \\


Option: 4

\frac{2(M+2 m)}{M}


Answers (1)

best_answer

\mathrm{L_{i}=I\omega }                             \mathrm{L_{f}=(MR^{2}+2MR^{2})\omega ^{1}}

       =\mathrm{MR^{2}\omega }                                               

By angular momentum conservation,
\mathrm{L_{i}= L_{f}}
\mathrm{MR^{2}\omega = \left ( MR^{2}+2mR^{2} \right ){\omega }'}
\mathrm{{\omega }'= \frac{M\omega }{\left ( M+2m \right )}}
\mathrm{{\therefore {\omega }'= \frac{2M}{\left ( M+2m \right )}}
The correct option is (3)  
 

Posted by

jitender.kumar

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