Question

A ball is moving with uniform speed in a circular path of radius $3\text{m}$ at a rate of $5\text{revolution/minute}$. Find the average speed of the ball.

• A. $\frac{3\pi }{2}\text{m/s}$
• B. $15\pi \text{m/s}$
• C. $5\pi \text{m/s}$
• D. $\frac{\pi }{2}\text{m/s}$

Answer 1

The correct option is D $\frac{\pi }{2}\text{m/s}$

The ball is moving such that it completes $5$ revolutions in a time interval of $1\text{minute}$.
In one complete revolution, the ball will travel the distance equal to the perimeter of the circular path.
$\Rightarrow \text{Total distance covered}\left(S\right)=5\times 2\pi r$
$\Rightarrow {\text{Velocity}}_{\text{avg}}=\frac{S}{\Delta t}$
$\Rightarrow {\text{Velocity}}_{\text{avg}}=\frac{10\times \pi \times 3\text{m}}{60\text{s}}$
$\therefore {\text{Velocity}}_{\text{avg}}=\frac{\pi }{2}\text{m/s}$