Question

A particle is initially at rest, moves along in a circle of radius $R=2\text{m}$ with an angular acceleration $\alpha =\frac{\pi }{8}{\text{rad/sec}}^2$. The magnitude of average velocity of the particle over the time it moves by half of the circle is

• A. $4\text{m/s}$
• B. $3\text{m/s}$
• C. $2\text{m/s}$
• D. $1\text{m/s}$

Answer 1

The correct option is D $1\text{m/s}$

Tangential acceleration $a_t=R\alpha =2\times \frac{\pi }{8}=\frac{\pi }{4}{\text{m/sec}}^2$
$\therefore$ Distance travelled in time ${}^{\prime }{t}^{\prime }$ is given by $s=\frac{1}{2}{a}_t{t}^2=\frac{\pi t^2}{8}$

For a half circle, distance travelled $s=\pi R$
Hence, $\pi R=\frac{\pi t^2}{8}$
$\Rightarrow 2\pi =\frac{\pi t^2}{8}$
$\Rightarrow t^2=16$ (or) $t=4s$

$\therefore$ Average velocity $=\frac{\text{Total displacement}}{\text{Time}}=\frac{2R}{4}=1\text{m/s}$