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

The Correct Option is C

$\alpha $ is constant
$\alpha = \frac{\omega_1^2 - \omega_2^2}{2 \theta}$
$\frac{\omega - \left( \frac{\omega}{2} \right)^2 }{2 \theta_1} = \frac{\left( \frac{\omega}{2}\right)^2 - 0}{2\theta_2}$
$\theta_2 = \frac{\theta_1}{3}$

Answer 2

\(ω_1^2-ω_2^2= 2αθ\)

\(ω^2-(\frac ω2)^2= 2α \times 120\)
\(\frac {3ω^2}{4}=240α\)

\(\frac {ω^2}{4}=80α\)   ………. (1)
No. of rotations further made = n
\(\frac {ω^2}{4}=2αn\)
From eq (1)
\(80α=2αn\)
\(n=40\)

So, the correct option is (C): 40