Q150 / 150 · MHT CET 2023 (10 May Shift 2) · Physics

A particle performing uniform circular motion of radius $\frac{\pi}{2} \mathrm{~m}$ makes ' $\mathrm{x}$ ' revolutions in time ' $\mathrm{t}$ '. Its tangential velocity is

  • A
    $\frac{\pi \mathrm{X}}{\mathrm{t}}$
  • B
    $\frac{\pi \mathrm{x}^2}{\mathrm{t}}$
  • C
    $\frac{\pi^2 x^2}{t}$
  • Correct answer
    D
    $\frac{\pi^2 x}{t}$

Solution

$\begin{aligned} & \text { Circumference of the circle }=2 \pi \mathrm{r} \\ & \therefore \quad \text { Tangential velocity }=\frac{\text { Distance Travelled }}{\text { Time }} \\ & \qquad \frac{\pi^2 \times x}{\mathrm{t}} \\ & =\frac{\pi^2 x}{\mathrm{t}}\end{aligned}$

Hence, the correct answer is option: 'D'.

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