A Particle of mass 'M' moves in a uniform circular path of radius 'r' with a constant speed 'v' then its centripetal acceleration is .

Options

A. `(v^(2))/(r)`
B. `(v^(2))/(r^(2))`
C. `v^(2) r`
D. Zero

Answer

To find the centripetal acceleration of a particle moving in a uniform circular path, we can use the formula for centripetal acceleration, which is given by:

\[ a_c = \frac{v^2}{r} \]

Where:
- \( a_c \) is the centripetal acceleration,
- \( v \) is the constant speed of the particle,
- \( r \) is the radius of the circular path.

### Step-by-Step Solution:

1. **Identify the Given Variables**:
- Mass of the particle: \( M \) (not needed for centripetal acceleration)
- Radius of the circular path: \( r \)
- Constant speed of the particle: \( v \)

2. **Recall the Formula for Centripetal Acceleration**:
The formula for centripetal acceleration is:
\[ a_c = \frac{v^2}{r} \]

3. **Substitute the Known Values**:
Since we have the values for \( v \) and \( r \), we can substitute them into the formula:
\[ a_c = \frac{v^2}{r} \]

4. **Final Expression**:
Therefore, the centripetal acceleration of the particle moving in a uniform circular path is:
\[ a_c = \frac{v^2}{r} \]

### Final Answer:
The centripetal acceleration is \( \frac{v^2}{r} \).

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