Question

If the frequency of the rotating platform is $f$ and the distance of a boy from the centre is $r,$ what is the area swept out per second by the line connecting the boy to the centre?

• A. $\pi r f$
• B. $2 \pi r f$
• C. $\pi r^{2} f$
• D. $2 \pi r^{2} f$

Answer 1

Answer: (C)

Area of sector $(A)=\frac{1}{2} r^{2} \theta$
$\frac{dA}{dt}=\frac{1}{2} r^{2} \frac{d \theta}{d t}=\frac{r^{2}}{2} \cdot \omega=\frac{r^{2}}{2}(2 \pi f)=\pi r^{2} f$