Question

A particle performing uniform circular motion of radius $\frac{\pi}{2} \text{ m}$ makes $x$ revolutions in time $t$. Its tangential velocity is

• A. $\frac{x}{\pi t}$
• B. $\frac{\pi^2}{x t}$
• C. $\frac{\pi^2 x}{t}$
• D. $\frac{\pi x}{t}$

Hint:

Distance in $x$ revolutions is $x(2\pi r)$. Velocity is total distance divided by time.

Answer 1

The Correct Option is C

Step 1: Concept
Tangential velocity $v = r\omega$, where $\omega = 2\pi f$ is angular velocity.

Step 2: Meaning
Frequency $f = \text{number of revolutions} / \text{time} = x/t$.

Step 3: Analysis
$v = r(2\pi f) = (\frac{\pi}{2})(2\pi)(\frac{x}{t})$. The 2's cancel out.

Step 4: Conclusion
$v = \frac{\pi^2 x}{t}$. Final Answer: (C)