# Initial angular velocity of a circular disc of mass  M  is    . Then two small spheres of mass  are attached gently to two diametrically opposite points on the edge of the disc What is the final angular velocity of the disc ? Option 1) Option 2) Option 3) Option 4)

As we learn in

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 .

$L_{1}=L_{2}\; \Rightarrow I_{1}\omega {}_{1}=I_{2}\omega {}_{2}$

$I_{1}=\frac{1}{3}mR^{2}$

$I_{2}=\frac{1}{2}mR^{2}+2mR^{2}$

$\frac{1}{2}mR^{2}\omega_{1}=\frac{MR^{2}+4mR^{2}}{2} \;\omega {}_{2}$

$\omega{}_{2}=\frac{M\omega{}_{1}}{M+4m}$

Option 1)

This is an incorrect option.

Option 2)

This is an incorrect option.

Option 3)

This is the correct option.

Option 4)

This is an incorrect option.

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