Question

Which of the following graphs correctly represent a particle moving on a horizontal circle with angular acceleration of the particle directly proportional to $t$? Assume that the particle starts from rest.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given angular acceleration $\left(\alpha \right)$ is proportional to $t$
$\Rightarrow \alpha =\frac{d\omega }{dt}=kt$
$\Rightarrow \frac{d\omega }{dt}\propto t$
Hence slope increases with time.
$\Rightarrow \omega =\frac{k{t}^2}{2}+C=\frac{k{t}^2}{2}$
(because $\omega =0$ at $t=0$)
$\Rightarrow \omega \propto t^2$
$\therefore$ Option (c) is correct.