Question

Speed of a body in uniform circular motion for radius, $R$ and time period, $T$ is given by:

• A. $\frac{R}{T}$
• B. $\frac{\pi R}{T}$
• C. $\frac{2\pi R}{T}$
• D. $\frac{R}{2\pi T}$

Answer 1

The correct option is C $\frac{2\pi R}{T}$

For a body in uniform circular motion, speed is constant. Also, it is periodic.

Distance covered in one revolution equals the circumference of the circle in which it orbits. Hence, distance travelled in one revolution is:
$s=2\pi R$

Time period is the time taken for the body to complete one revolution. Here, it is given to be equal to $T$.

Speed is given by the ratio of distance and time. Hence, speed of body in uniform circular motion is given by:
$v=\frac{s}{T}$
$v=\frac{2\pi R}{T}$