Question

A disc of mass $2kg$ and radius $0.2m$ is rotating with angular velocity $39rad$ $s^{-1}$. What is angular velocity, if two masses each of $0.25kg$ is put on periphery of the disc?

• A. $24rad$ $s^{-1}$
• B. $36rad$ $s^{-1}$
• C. $15rad$ $s^{-1}$
• D. $26rad$ $s^{-1}$

Answer 1

The correct option is A $24rad$ $s^{-1}$

Angular momentum in absence of any external torque remains constant. If no external torque acts on a system of particles, then angular momentum of the system remains constant,

$i.e,\tau =0⟹\frac{dL}{dt}=0⟹L=I\omega =constant$

Initial angular momentum = Final angular momentum

$⟹I_1{\omega }_1=I_2{\omega }_2$

$\therefore \frac{1}{2}M{r}^2{\omega }_1=\frac{1}{2}(M+2m)r^2{\omega }^2...\left(i\right)$

Here, $M=2kg,m=0.25kg,r=0.2m,{\omega }_1=30rad/s$

Hence, we get after putting the given values in Eq.(i)

$⟹\frac{1}{2}\times 2\times (0.2{)}^2\times 30=\frac{1}{2}\times (2+2\times 0.25\left)\right(0.2{)}^2\times {\omega }_2$

$⟹1.2=0.05{\omega }_2⟹{\omega }_2=24rad/s$