MCQ
A disc rotating about its axis from rest, acquires the angular speed $100 \,rev/s$ in $4$ second. The angle rotated by it during these four seconds (in radian) is ...... $\pi$
- A$100$
- B$200$
- C$300$
- ✓$400$
✓
Answer
Correct option: D.
$400$
d
(d)
(d)
Initial angular speed, $\omega_0=0 rad / s$
Final angular speed, $\omega=100 rps$
$\Rightarrow \omega=100 \times 2 \pi rad$ $\Rightarrow \omega=200 \pi rad / s$
Time, $t=4 s$
From kinematics:
$\omega =\omega_0+\alpha t$
$\Rightarrow 200 \pi=4 \alpha$
$\Rightarrow \alpha=\frac{200 \pi}{4} rad / s ^2$
where, $\alpha$ is angular acceleration.
Also,
$\theta =\omega_0 t+\frac{1}{2} \alpha t^2$
$\Rightarrow \theta =0+\frac{1}{2} \times \frac{200 \pi}{4} \times 16$
$\Rightarrow \theta =400 \pi$
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