A disc is rotating with an angular velocity _0. A constant retrar… - Vidyadip

MCQ

A disc is rotating with an angular velocity $\omega _0. $ A constant retrarding torque is applied on it to stop the disc. The angular velocity becomes $(\omega _0/2)$ after $n$ rotations. How many more rotations will it make before coming to rest ?

A
$n$
B
$2n$
C
$\frac {n}{2}$
✓
$\frac {n}{3}$

✓

Answer

Correct option: D.

$\frac {n}{3}$

d
$w^{2}=w_{0}^{2}-2 \alpha \theta$

$\left(w_{0} / 2\right)^{2}=w_{0}^{2}-2\alpha Q$

$\left(w_{0} / 2\right)^{2}=w_{0}^{2}-2 \alpha Q_{1}$

$0=\left(w_{0} / 2\right)^{2}-2 \alpha Q_{2}$

$Q_{2}=\frac{Q_{1}}{3}$

$\Rightarrow \frac {n}{3}$

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