Question

A disc of mass '$m$' and radius '$R$' is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass $m/2$ each are placed in it on either side of the centre of the disc as shown in figure. The disc is given an initial angular velocity ${\omega }_0$ and released. The angular speed of the disc when the balls reach the end of the disc is:

• A. $\frac{{\omega }_0}{2}$
• B. $\frac{{\omega }_0}{3}$
• C. $\frac{{2\omega }_0}{3}$
• D. $\frac{{\omega }_0}{4}$

Answer 1

The correct option is B $\frac{{\omega }_0}{3}$

Let the final angular velocity of the disc be $\omega$.

Angular momentum about the center of the disc is conserved, $L_i=L_f$

$I_{Disc}{w}_o+0=I_{Disc}w+2\times \left(\frac{m}{2}\right)R^{2}w$

$\frac{1}{2}m{R}^2{w}_o+0=\frac{1}{2}m{R}^{2}w+2\times \left(\frac{m}{2}\right)R^{2}w$

$⟹w=\frac{w_o}{3}$