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

Options

A. `25 m//s^(2)`
B. `36 m//s^(2)`
C. `5 m//s^(2)`
D. `15 m//s^(2)`

Answer

To find the acceleration of a particle moving in a circle with a given radius and time period, we can follow these steps:

### Step 1: Identify the given values
- Radius (R) = 5 cm = 0.05 m (convert to meters)
- Time period (T) = 0.2π seconds

### Step 2: Calculate the angular velocity (ω)
The angular velocity can be calculated using the formula:
\[ \omega = \frac{2\pi}{T} \]
Substituting the value of T:
\[ \omega = \frac{2\pi}{0.2\pi} \]
The π cancels out:
\[ \omega = \frac{2}{0.2} = 10 \text{ rad/s} \]

### Step 3: Determine the radial (centripetal) acceleration (a_c)
The radial acceleration for circular motion is given by the formula:
\[ a_c = \omega^2 R \]
Substituting the values of ω and R:
\[ a_c = (10 \text{ rad/s})^2 \times 0.05 \text{ m} \]
Calculating this gives:
\[ a_c = 100 \times 0.05 = 5 \text{ m/s}^2 \]

### Final Answer:
The acceleration of the particle is \(5 \text{ m/s}^2\).

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