Question

A particle is moving with a constant speed $v$ in a circle. What is the magnitude of average velocity after half rotation ?

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

Answer 1

Answer: (B)

$\frac{2v}{\pi}$

Answer 2

We are given that a particle is moving with a constant speed $\nu$ in the circle so the time taken to cover the complete circle would be equal to $T = \frac{2\pi r}{\nu}$ hence the time taken to cover half the rotation would be equal to $T_{1/2} = \frac{2\pi r}{2\nu} = \frac{\pi r}{\nu}$ , hence the magnitude of average velocity after half rotation on would be equal to $\nu_{av} = \frac{2r}{\frac{\pi r}{\nu}} = \frac{2\nu}{\pi}$