A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches…
A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches the end of diameter in 3 second. The angular speed of the body in rad $/ \mathrm{s}$ is
$\frac{\pi}{2}$
$\frac{\pi}{3}$
$\frac{\pi}{4}$
$\frac{\pi}{5}$
Solution
Let $r$ be radius,
Circumference $=2 \pi$,
Half the circle is covered,
$\therefore \quad$ Distance covered $=\pi r=15 r$
...(given, $\mathrm{r}=15 \mathrm{~cm}$ )
Speed $=\frac{\text { distance }}{\text { time }}=\frac{15 \pi}{3}=5 \pi$
Angular speed, $\theta=\frac{\mathrm{v}}{\mathrm{r}}=\frac{5 \pi}{15}=\frac{\pi}{3} \mathrm{rad} / \mathrm{s}$