Question

Two wheels are mounted side by side and each is marked with a dot on its rim. The two dots are aligned with the wheels at rest, then one wheel is given a constant angular acceleration of $\frac{\pi }{2}{\text{rad/s}}^2$ and the other $\frac{\pi }{4}{\text{rad/s}}^2$. Then the two dots become aligned again for the first time after

• A. 2 seconds
• B. 4 seconds
• C. 1 seconds
• D. 8 seconds

Answer 1

The correct option is B 4 seconds

Suppose dots again come in coincidence after a time t.
This happens if the slower disc makes one rotation less than the other.
$\therefore 2\pi n=\frac{1}{2}\times \frac{\pi }{2}{t}^2\left(1\right)$
and $2\pi (n-1)=\frac{1}{2}\times \frac{\pi }{4}{t}^2\left(2\right)$
Dividing Eq. (1) by Eq. (2), we get;
$\frac{n}{n-1}=\frac{2}{1}$ or n = 2
Putting n = 2 in Eq. (1), we get;
t = 4 seconds
Hence, the correct answer is option (b).