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 $ 2\,t $ 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 $=t \,sec$ )
$15^{\circ}=0+\frac{1}{2} \alpha t^{2} $
$\Rightarrow 15^{\circ}=\frac{1}{2} \alpha t^{2}\,\,\,...(i)$
For the second conditions (time $=3 t\, sec$ )
$\theta_{1}=\frac{1}{2} \alpha(3 t)^{2}=\frac{1}{2}(\alpha) 9 t^{2}\,\,\,...(ii)$
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))