Question

A disc having mass M and radius R is rotating with angular velocity $\omega$ , another disc of mass 2M and radius R/2 is placed coaxially on the first disc gently. The angular velocity of system will now be:

• A. $\frac{4\omega }{5}$
• B. $\frac{2\omega }{5}$
• C. $\frac{3\omega }{2}$
• D. $\frac{2\omega }{3}$

Answer 1

Answer: (D)

First, we find out the moment of inertia of the disc about the axis passing the centre and normal to through the plane is $I=\frac{M{R}^2}{2}$ So, for first disc $I_1=\frac{M{R}^2}{2}$ Similarly, for second disc $I_2=\frac{2M}{2}{\left(\frac{R}{2}\right)}^2=\frac{M{R}^2}{4}$ Total moment of inertia of the whole system $I=I_1+I_2=\frac{M{R}^2}{2}+\frac{M{R}^2}{4}=\frac{3}{4}M{R}^2$ According to the conservation of angular momentum $I_1\omega =I\omega$ $\frac{M{R}^2}{2}\times \omega =\frac{3}{4}M{R}^2\times \omega$ So, $\omega =\frac{2}{3}\omega$