Question

A particle starting from rest moves along the circumference of a circle of radius r =$\sqrt{2}$ m and angular acceleration $\alpha$ = $\frac{\pi }{4}$ rad /s${}^2$ .What is the magnitude of its average velocity in the times it completes a quarter rotation ?

• A. $\frac{\pi }{\sqrt{2}}$ m /s
• B. $\frac{\pi }{2\sqrt{2}}$ m/s
• C. $\frac{2\sqrt{2}}{\pi }$ m/ s
• D. $\frac{\pi }{2}$ m/s

Answer 1

Answer: (D)

$\frac{\pi }{2}$ m/s

Given,

${\omega }_0=0rad/s$

$r=\sqrt{2}m$

$\alpha =\frac{\pi }{4}rad/s^2$

$\theta =\frac{\pi }{2}rad$

The angular displacement is given by

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$\frac{\pi }{2}=\frac{1}{2}\frac{\pi }{4}{t}^2$

$t=2sec$

Displacement, $PQ=\sqrt{r^2+r^2}=\sqrt{2}rm$

The average velocity,

$v_{avg}=\frac{displacement}{time}$

$v_{avg}=\frac{\sqrt{2}r}{2}$

$v_{avg}=\frac{\sqrt{2}.\sqrt{2}}{2}$

$v_{avg}=1m/s$