Question

A disc of mass 2 kg arid radius 0.2 m is rotating with angular velocity 30 rads${}^{-1}$. What is angular velocity, if a Mass of 0.25 kg is put on periphery of the disc?

• A. 24 rad $s^{-1}$
• B. 36 rad $s^{-1}$
• C. 15 rad $s^{-1}$
• D. 26 rad $s^{-1}$

Answer 1

The correct option is A 24 rad $s^{-1}$

When there is no external torque then the angular momentum remains constant.

i.e. $r=0\frac{dL}{dt}=0$

$\therefore I_1{\omega }_1=I_2{\omega }_2$ ...(i)

Here M = 2 kg, m = 0.25 kg, r = 0.2 m, ${\omega }_1=30rad{s}^{-1}$

Hence, putting the value of ${\omega }_1$ in Eq. (i), we get

$\frac{1}{2}\times 2\times (0.2{)}^2\times 30=\frac{1}{2}\times (2+2\times 0.25\left)\right(0.2{)}^2\times {\omega }_2$

$1.2=0.05{\omega }_2$

${\omega }_2=24rad{s}^{-1}$