Question

A particle performing U.C.M. of radius \(\frac{π}{2}\) m makes 'x' revolutions in time t. Its tangential velocity is

• A. \(\frac{πx}{t}\)
• B. \(\frac{π^2x}{t}\)
• C. \(\frac{π}{xt}\)
• D. \(\frac{xt}{π}\)

Hint:

Speed = distance per revolution times revolutions per time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In uniform circular motion, tangential speed is \(v=\omega r\) and \(\omega=\dfrac{2\pi}{T}\).

Step 2: Find the period:
\(x\) revolutions take time \(t\), so one revolution takes \(T=\dfrac tx\). Then \(\omega=\dfrac{2\pi x}t\).

Step 3: Find the speed:
\[ v=\omega r=\frac{2\pi x}{t}\times\frac\pi2=\frac{\pi^2x}{t} \]

Step 4: Choose:
Option (B).

Final Answer:
The tangential velocity is pi squared x over t. \[ \boxed{\frac{\pi^2x}{t}} \]