Question

The angular velocity of the disc after the particle sticks to it is

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

Answer 1

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

Angular momentum about O is conserved i-e $L_i=L_f$

Let the final angular velocity of the system be $w^{\prime }$.

$Iw+0=I{w}^{\prime }+m{R}^2{w}^{\prime }$

$\frac{1}{2}m{R}^{2}w=\frac{1}{2}m{R}^2{w}^{\prime }+m{R}^2{w}^{\prime }$

$w^{\prime }=\frac{w}{3}$