A particle performing U.C.M. of radius $\frac{\pi}{2} \mathrm{~m}$ makes ' $\mathrm{x}$ ' revolutions in…

A particle performing U.C.M. of radius $\frac{\pi}{2} \mathrm{~m}$ makes ' $\mathrm{x}$ ' revolutions in time ' $\mathrm{t}^{\prime}$. Its tangential velocity is
  1. $\frac{\pi t}{x^{2}}$
  2. $\frac{\pi \mathrm{x}^{2}}{\mathrm{t}}$
  3. $\frac{\pi \mathrm{X}}{\mathrm{t}^{2}}$
  4. $\frac{\pi^{2} x}{t}$

Solution

frequency $f=\frac{x}{t}, \omega=2 \pi f=\frac{2 \pi x}{t}$ tangential velocity $V=\omega r=\frac{2 \pi x}{t} \cdot \frac{\pi}{2}=\frac{\pi^{2} x}{t}=3$

Asked in: MHT CET 2020 (13 Oct Shift 1)

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