A stone whirled at the end of rope \(35 \mathrm{~cm}\) long, makes 15 complete revolutions in \(4 \mathrm{~seconds}\). Find the angular velocity in radius per second.
A. 23.6rad.s \(\mathrm{s}^{-1}\) B. \(31.4 \mathrm{rad} . \mathrm{s}^{-1} \) C. \(824.7 \mathrm{rad} . \mathrm{s}^{-1} \) D. 942.0rad.s \({ }^{-1}\)
Correct Answer: A
Explanation
\(t=4 s\) Number of revolutions \(=15\) since \(1 \mathrm{rev}=2 \pi \mathrm{rad}, 15\) revolutions \(=2 \pi \mathrm{rad} \times 15=30 \pi \mathrm{rad}\) \(=\left(30 \times \frac{22}{7}\right) \mathrm{rad}=94.286 \mathrm{rad}\) \(\omega=\frac{\theta}{t}=\frac{94.286 \mathrm{rad}}{4 \mathrm{~s}}\)
