Question

A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is $T$. In a time $t=\frac{T}{6}$, average speed of the particle is:

• A. $\frac{\pi R}{6T}$
• B. $\frac{2\pi R}{3T}$
• C. $\frac{2\pi R}{T}$
• D. $\frac{R}{T}$

Answer 1

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

In $t=\frac{T}{6}$, particle will travel ${\frac{1}{6}}^{\text{th}}$of the circle.


Hence,
$\text{Average speed}=\frac{\text{arc PQ}}{\text{time}}$

$\text{Average speed}=\frac{\frac{2\pi R}{6}}{\left(\frac{T}{6}\right)}=\frac{2\pi R}{T}$

Alternative: Since, average speed remains constant and the time required to make a full circle is $T$. So,

$\text{Average speed}=\frac{\text{Distance}}{\text{Time}}=\frac{2\pi R}{T}$

Hence, option $\left(\text{C}\right)$ is the correct answer.