Question

A particle performing U.C.M. of radius \( \dfrac{\pi}{2}\,\text{m} \) makes \(x\) revolutions in time \(t\). Its tangential velocity is

• A. \( \dfrac{\pi t}{x^2} \)
• B. \( \dfrac{\pi x^2}{t} \)
• C. \( \dfrac{\pi x}{t^2} \)
• D. \( \dfrac{\pi^2 x}{t} \)

Hint:

Always convert revolutions into radians while calculating angular velocity.

Answer 1

The Correct Option is D

Step 1: Expression for tangential velocity.
Tangential velocity in uniform circular motion is \[ v = \omega r \]

Step 2: Find angular velocity.
If the particle completes \(x\) revolutions in time \(t\), \[ \omega = \frac{2\pi x}{t} \]

Step 3: Substitute given radius.
\[ r = \frac{\pi}{2} \] \[ v = \frac{2\pi x}{t} \times \frac{\pi}{2} = \frac{\pi^2 x}{t} \]