Question

A disc which is at rest started to spin about a stationary axis. The angular acceleration of the disc is given by $\alpha =2\theta rad/s$, where $\theta$ is the angle of rotation of disc from its initial position. Which of the following graphs correctly represents the variation of angular velocity with respect to '$\theta$' ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Given $\alpha =2\theta$
We know $\alpha =\frac{d\omega }{dt}=\frac{d\omega }{d\theta }\times \frac{d\theta }{dt}$
$\Rightarrow \omega \frac{d\omega }{d\theta }=2\theta$
$\Rightarrow \omega d\omega =2\theta d\theta$
Integrating on both sides,
${\int }_0^{\omega }\omega d\omega ={\int }_0^{\theta }2\theta d\theta$
$\Rightarrow \frac{{\omega }^2}{2}=2\frac{{\theta }^2}{2}$
$\Rightarrow w=\sqrt{2}\theta$
Therefore, graph is a straight line passing through origin. (option b)