Question

A particle describes uniform circular motion in a circle of radius $2\, m$, with the angular speed of $2\, rad\, s^{-1}$ . The magnitude of the change in its velocity in $\frac{\pi}{2} s$ is

• A. $0 \,ms^{-1}$
• B. $2\sqrt{2} \,ms^{-1}$
• C. $8 \,ms^{-1}$
• D. $4 \,ms^{-1}$
• E. $4\sqrt{2} \,ms^{-1}$

Answer 1

Answer: (C)

Given, $r=2 \,m , \omega=2\, rad s ^{-1}, t=\frac{\pi}{2} \,S$
Now, $ \theta=\omega t=\pi\, rad$
$ V =r \omega=2 \times 2 $
$ V =4 \,ms ^{-1} $
Now, $ \Delta \,v=2 v \sin \frac{\theta}{2} $
$ \Delta \,v =2 \times 4 \times \sin \frac{\pi}{2} $
$ \Delta \,v =8 \,ms ^{-1} $