A particle performing uniform circular motion of radius π/2 m makes ' x ' revolutions in time ' t '. Its tangential velocity is (a) (π x)/(t) (b) (π x²)/(t) (c) (π² x²)/(t) (d) (π² x)/(t)

Answer: (d). ω = (2π x)/(t) for x revolutions in time t. v = rω = π/2 · (2π x)/(t) = (π² x)/(t). So the answer is (d) (π² x)/(t).

A particle performing uniform circular motion of radius π/2 m makes '… | MHT CET 2023 (10 May, Shift 2)

Q22MHT CET 2023 · 10 MAY · SHIFT 2Easy

Angular Variables

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

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Answer: (d)

$\omega = \frac{2\pi x}{t}$ for $x$ revolutions in time $t$ .
$v = r\omega = \frac{\pi}{2} \cdot \frac{2\pi x}{t} = \frac{\pi^2 x}{t}$ .
So the answer is (d) $\frac{\pi^2 x}{t}$ .

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