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

A particle performing U.C.M. of radius $\frac{\pi}{2} \mathrm{~m}$ makes ${ }_x$ revolutions in time $t$. Its tangential velocity is
  1. $\frac{\pi x}{t}$
  2. $\frac{\pi^2 x}{t}$
  3. $\frac{\pi^2 x^2}{t}$
  4. $\frac{2 \pi x}{t}$

Solution

Particle is under uniform circular motion, So angular velocity is $\omega=\frac{2 \pi x}{t}$ The tangential velocity is $v=\omega R=\left(\frac{2 \pi x}{t}\right) R$ Given, $R=\frac{\pi}{2}$, therefore, $v=\frac{\pi^2 x}{t}$

Asked in: MHT CET 2022 (10 Aug Shift 1)

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