A particle performing U.C.M. of radius frac{p | vedclass

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(B) The particle is performing uniform circular motion $(U.C.M.)$. The total angle covered in $x$ revolutions is $	heta = 2 \pi x$ radians. The angul

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$\frac{\pi^2 x}{t}$

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(B) The particle is performing uniform circular motion $(U.C.M.)$. The total angle covered in $x$ revolutions is $	heta = 2 \pi x$ radians. The angular velocity $\omega$ is given by $\omega = \frac{	heta}{t} = \frac{2 \pi x}{t}$. The tangential velocity $v$ is related to angular velocity by $v = \omega R$. Given the radius $R = \frac{\pi}{2} \ m$. Substituting the values,$v = \left( \frac{2 \pi x}{t} ight) 	imes \left( \frac{\pi}{2} ight) = \frac{\pi^2 x}{t} \ m/s$.

$A$ particle performing $U.C.M.$ of radius $\frac{\pi}{2} \ m$ makes $x$ revolutions in time $t$. Its tangential velocity is

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