Question

A particle is moving in a circle of radius $R$ with constant speed. The time period of particle is $T=1s$. In a time $t=\frac{T}{6}$ , the difference between the average speed and the average velocity of the particle is $2m/s$. Find the radius $R$ (in meters) of the circle. (Take $\pi =\frac{22}{7}$)

Answer 1

Angle rotated by particle in $\frac{T}{6}$ time will be
$\frac{2\pi }{6}=\frac{\pi }{3}rad$
Step 2: Find average speed
The average speed is given by,

$v_{\text{avg}}=\frac{\text{Displacement}}{\text{time}}$
$v_{avg}=\frac{2\pi R}{T}=\frac{2\pi R}{1}$
$v_{avg}=2\pi Rm/s$
Step 3: Find Average velocity

As we can see in figure each angle in triangle will be 60°, hence it forms an equilateral triangle so each side will be of same length which is $R$
Then the average velocity is

$\left|{\overrightarrow{v}}_{\text{avg}}\right|=\frac{\text{displacement}}{\text{time}}$


$\left|{\overrightarrow{v}}_{\text{avg}}\right|=\frac{R}{T/6}=6Rm/s$
Difference between average speed and average velocity
$=2\pi R-6R$

$2\pi -6)R$
$2=(2\times \frac{22}{7}-6)R$
$2=\left(\frac{2}{7}\right)R$
$\therefore R=7m$

Final Answer: 7