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: Distance method:
Distance in one revolution is $2\pi r=2\pi\cdot\frac\pi2=\pi^2$.

Step 2: Total distance:
In $x$ revolutions: $x\pi^2$.

Step 3: Speed:
$v=\dfrac{\text{distance}}{\text{time}}=\dfrac{\pi^2x}{t}$. Option (B).

Final Answer:
Distance in x turns divided by t. \[ \boxed{B} \]