Question

A circular disc is rotating about its own axis at uniform angular velocity $\omega$. The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $\frac{\omega }{2}$ during $120$ rotations. The number of rotations further made by it before coming to rest is:

• A. $120$
• B. $60$
• C. $40$
• D. $20$

Answer 1

Answer: (C)

$40$

${\omega }_1^2-{\omega }_2^2=2\alpha \theta$
$\Rightarrow (\omega {)}^2-{\left(\frac{\omega }{2}\right)}^2=2\alpha (120)$
$\Rightarrow \frac{3{\omega }^2}{4}=240\alpha$
No. of rotations further made$=n$
$\Rightarrow \frac{{\omega }^2}{4}=2\alpha \left(n\right)$
$3=\frac{240}{2n}$
$n=40$