Question

A wheel initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle $\theta_{1}$ in first one second and through an additional angle $\theta_{2}$in the next one second. The ratio $\frac{\theta_{2}}{\theta_{1}}$ is

• A. 4
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (C)

3

Answer 2

Angular displacement in first one second

$\theta_{1} = \frac{1}{2}\alpha(1)^{2} = \frac{\alpha}{2}$ ......(i) [From $\theta = \omega_{1}t + \frac{1}{2}\alpha t^{2}$]

Now again we will consider motion from the rest and angular displacement in total two seconds

$\theta_{1} + \theta_{2} = \frac{1}{2}\alpha(2)^{2} = 2\alpha$ ......(ii)

Solving (i) and (ii) we get $\theta_{1} = \frac{\alpha}{2}$ and $\theta_{2} = \frac{3\alpha}{2}$

$\therefore$ $\frac{\theta_{2}}{\theta_{1}} = 3$.