Q. A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle $\theta_{1}$ in the first 2 s , in the next 2 s, it rotates through an additional angle $\theta_{2}$, the ratio of $\frac{\theta_{2}}{\theta_{1}}$ is
A) 1
B) 2
C) 3
D) 5
Explanation
(c) $\alpha = \frac{\omega_{\ }^{\ }}{t}$ and $\omega = \frac{\theta}{t}$
$\therefore\ \alpha = \frac{\theta}{t^{2}}$
But $\alpha =$constant
So, $\frac{\theta_{1}}{\theta_{1} + \theta_{2}} = \frac{(2)^{2}}{(2 + 2)^{2}}$
or $\frac{\theta_{1}}{\theta_{1} + \theta_{2}} = \frac{1}{4}$
or $\frac{\theta_{1} + \theta_{2}}{\theta_{1}} = \frac{4}{1}$
or $1 + \frac{\theta_{2}}{\theta_{1}} = \frac{4}{1}$
$\therefore\ \ \frac{\theta_{2}}{\theta_{1}} = 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.