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Help me solve this A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω . Two objects, each of mass m are attached gently to the opposite ends of the diameter of the ring. The wheel now rotat

A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω . Two objects, each of mass m are attached gently to the opposite ends of the diameter of the ring. The wheel now rotates with an angular velocity.

  • Option 1)

    ω M/(M + m)

  • Option 2)

    {(M – 2m)/(M +2m)}ω

  • Option 3)

    {M/(M + 2m)}ω

  • Option 4)

    {(M + 2m)/M} ω

 
Answers (1)
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As we discussed in concept

Law of conservation of angular moment -

\vec{\tau }= \frac{\vec{dL}}

- wherein

If net torque is zero

i.e. \frac{\vec{dL}}= 0

\vec{L}= constant

angular momentum is conserved only when external torque is zero .

 

 L_{i}=L_{t}

I_{1}w=I_{2}{w}'

mr^{2}w=(m+2m)r^{2}{w}'

{w}'=\frac{Mw}{m+2m}

 


Option 1)

ω M/(M + m)

This is incorrect option

Option 2)

{(M – 2m)/(M +2m)}ω

This is incorrect option

Option 3)

{M/(M + 2m)}ω

This is correct option

Option 4)

{(M + 2m)/M} ω

This is incorrect option

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