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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

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As we discussed in concept

Law of conservation of angular moment -

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

- wherein

If net torque is zero

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

$\vec{L}= constant$

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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