Question

A uniform disc of radius a and mass m, is rotating freely with angular speed $\omega$ in a horizontal plane about a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddenly attached to the rim of the disc and rotates with it. The new angular speed is

• A. $\frac{\omega }{6}$
• B. $\frac{\omega }{3}$
• C. $\frac{\omega }{2}$
• D. $\frac{\omega }{5}$

Answer 1

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

$I_1{\omega }_1=I_2{\omega }_2$
$\therefore {\omega }_2=\frac{I_1}{I_2}.{\omega }_1$
$=\frac{\left(\frac{1}{2}m{a}^2\right)}{\left(\frac{1}{2}m{a}^2\right)+m{a}^2}.\omega =\frac{\omega }{3}$