Question

A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in \( \text{m/s}^{2} \) is:

• A. $\pi^{2}$
• B. $8\pi^{2}$
• C. $4\pi^{2}$
• D. $2\pi^{2}$

Hint:

Acceleration in uniform circular motion is always directed toward the center.

Answer 1

The Correct Option is C

Step 1: Concept
Centripetal acceleration $a = \omega^{2}r$.
Step 2: Analysis
Frequency $\nu = 2 \text{ rps}$, so $\omega = 2\pi\nu = 4\pi \text{ rad/s}$. Radius $r = 0.25 \text{ m}$. $a = (4\pi)^{2} \times 0.25 = 16\pi^{2} \times 0.25$.
Step 3: Conclusion
$a = 4\pi^{2} \text{ m/s}^{2}$.
Final Answer: (C)