Question

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane ahout an axis passing through its centre and perpendicular to the plane with an angular velocity $\omega$ Another disc of same mass hut half the radius is gently placed over it coaxially. The angular speed o f the composite disc will be

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

Answer 1

Answer: (B)

$\frac{4}{5}\omega$

Answer 2

$I_1\omega_1=(I_1+I_2)\omega_2$ $\left[\frac{MR^2}{2}\right]\omega=\left[\frac{MR^2}{2}+\frac{M\left(\frac{R}{2}\right)^2}{2}\right]\omega^2$ $=\left[\frac{MR^2}{2}+\frac{MR^2}{8}\right]\omega_2=\left[\frac{5MR^2}{8}\right]$ $\omega_2=\frac{4}{5}\omega$