Question

A wheel which is initially at rest is subjected to a constant angular acceleration about its axis. It rotates through an angle of $15^{o}$ in time $t$ seconds. The increase in angle through which it rotates in the next $2t$ seconds is

• A. $90^{o}$
• B. $120^{o}$
• C. $30^{o}$
• D. $45^{o}$

Answer 1

Answer: (B)

If angular acceleration is constant, we have
$\theta =\omega _{0}t+\frac{1}{2}\alpha t^{2}$
The given $\theta =15^{o}$
$\omega _{0}=0$
For the first conditions (time = t sec)
$15^{o}=0+\frac{1}{2}\alpha t^{2}$
$\Rightarrow $ $15^{o}=\frac{1}{2}\alpha t^{2}$ ......(i)
For the second conditions (time = t+2t sec)
$\left(\theta \right)_{1}=\frac{1}{2}\alpha \left(3 t\right)^{2}=\frac{1}{2}\left(\alpha \right)9t^{2}$ .......(ii)
So for 2t sec, $\Delta \theta =\theta _{1}-\frac{1}{2}\alpha t^{2}$
$\Delta \theta =9\times \frac{1}{2}\alpha t^{2}-\frac{1}{2}\alpha t^{2}$
$=8\frac{1}{2}\alpha t^{2}$
$=8\times 15^{o}=120^{o}$ (from equation(i))