Question

A disc of mass $2\, kg$ and radius $0.2\, m$ is rotating with angular velocity $30 \, rad\,s^{-1}$ . What is angular velocity, if a mass of $0.25\, kg$ is put on periphery of the disc ?

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

Answer 1

Answer: (A)

When there is no external torque then the angular momentum remains constant.
i.e. $\tau=0 \frac{d L}{d t}=0$
$ \therefore \, I_{1} \omega_{1}=I_{2} \omega_{2} \,\,\,\,\,\dots(i)$
Here $M=2 \,kg , m =0.25 \,kg , r =0.2 \,m$
$\omega_{1}=30\, rad \,s ^{-1} $
Hence, putting the value of $\omega_{1}$ in Eq. (i), we get
$\frac{1}{2} \times 2 \times(0.2)^{2} \times 30=\frac{1}{2} \times(2+2 \times 0.25)(0.2)^{2} \times \omega_{2}$
$1.2=0.05 \,\omega_{2}$
$\omega_{2}=24 \,rad\, s ^{-1}$