Question

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\sec$, it rotates through an angle $\theta_{1}$. In the next $2\sec$, it rotates through an additional angle $\theta_{2}$. The ratio of $\theta_{1}/\theta_{2}$ is

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

Answer: (C)

3

Answer 2

From equation of motion$\theta = \omega_{1}t + \frac{1}{2}\alpha t^{2}$

$\theta_{1} = 0 + \frac{1}{2}\alpha(2)^{2}$= 2α …..(i)

[As $\omega_{1} = 0,$ $t = 2sec,\theta = \theta_{1}$]

For second condition

$\theta_{1} + \theta_{2} = 0 + \frac{1}{2}\alpha(4)^{2}$

[As $\omega_{1} = 0,$ $t = 2 + 2 = 4sec,\theta = \theta_{1} + \theta_{2}$]

$\theta_{1} + \theta_{2} = 8\alpha$….(ii)

From (i) and (ii) $\theta _ { 1 } = 2 \alpha$ $\theta_{2} = 6\alpha\therefore\frac{\theta_{2}}{\theta_{1}} = 3$