A particle starting from rest moves along the circumference of a circle of radius ' $\mathrm{r}^{\prime}$…

A particle starting from rest moves along the circumference of a circle of radius ' $\mathrm{r}^{\prime}$ with angular acceleration ' $\alpha^{\prime}$ '. The magnitude of the average velocity, in the time it completes the small angular displacement ' $\theta$ ' is
  1. $r\left(\frac{2}{\alpha \theta}\right)^{2}$
  2. $r\left(\frac{\alpha \theta}{2}\right)$
  3. $r\left(\frac{\alpha \theta}{2}\right)^{2}$
  4. $r\left(\frac{\alpha \theta}{2}\right)^{\frac{1}{2}}$

Solution

$S=r \theta$ $\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$ $\therefore t=\sqrt{\frac{2 \theta}{\alpha}}$ Average velocity $=\frac{\text { displacement }}{\text { time }}=\frac{r \theta}{\sqrt{\frac{2 \theta}{\alpha}}}$ $=r \sqrt{\frac{\alpha}{2 \theta}} \cdot \theta=r \sqrt{\frac{\alpha \theta}{2}}$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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