A particle moves in a circle of radius 5 cm with constant speed and time period 0.2π s. The acceleration of th

Question

A particle moves in a circle of radius 5 cm with constant speed and time period 0.2π s. The acceleration of the particle is:

Accepted Answer

1. **Identify Given Values:** 
   - Radius $R = 5 	ext{ cm} = 5 	imes 10^{-2} 	ext{ m}$.
   - Time Period $T = 0.2\pi 	ext{ s}$.
2. **Formula for Centripetal Acceleration:** For an object in uniform circular motion, the acceleration is centripetal and given by $a_c = \omega^2 R$, where $\omega$ is the angular velocity .
3. **Relate Angular Velocity to Time Period:** The relationship is $\omega = \frac{2\pi}{T}$ .
4. **Substitute and Calculate:**
   $$ a_c = \left( \frac{2\pi}{T} ight)^2 R $$
   $$ a_c = \left( \frac{2\pi}{0.2\pi} ight)^2 (5 	imes 10^{-2}) $$
   $$ a_c = \left( \frac{2}{0.2} ight)^2 (0.05) = (10)^2 (0.05) = 100 	imes 0.05 = 5 	ext{ m/s}^2 $$

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