Question

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

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

Answer 1

Answer: (B)

If angular acceleration is constant, we have
$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$
The given $\theta =15^{\circ }$
${\omega }_0=0$
For the first conditions (time $=tsec$ )
$15^{\circ }=0+\frac{1}{2}\alpha t^2$
$\Rightarrow 15^{\circ }=\frac{1}{2}\alpha t^2...(i)$
For the second conditions (time $=3tsec$ )
${\theta }_1=\frac{1}{2}\alpha (3t{)}^2=\frac{1}{2}(\alpha )9t^2...(ii)$
So, $\Delta \theta ={\theta }_1-\frac{1}{2}\alpha t^2$
$\Delta \theta =9\times \frac{1}{2}\alpha t^2-\frac{1}{2}\alpha t^2$
$=8\frac{1}{2}\alpha t^2$
$=8\times 15^{\circ }=120^{\circ }$ (from Eq. (i))