The dimensions of centripetal acceleration is

Options

A. `L^(2)//T^(2)`
B. `L^(2)//T`
C. `L//T^(-2)`
D. `1//T^(2)`

Answer

To find the dimensions of centripetal acceleration, we can start with the formula for centripetal acceleration:

1. **Formula for Centripetal Acceleration**:
\[ a_c = \frac{v^2}{r} \]
where \( a_c \) is the centripetal acceleration, \( v \) is the linear velocity, and \( r \) is the radius of the circular path.

2. **Express Velocity in Terms of Dimensions**:
The linear velocity \( v \) can be expressed as:
\[ v = \frac{\text{distance}}{\text{time}} = \frac{L}{T} \]
where \( L \) represents length and \( T \) represents time.

3. **Substituting Velocity into the Formula**:
Now, substituting \( v \) into the centripetal acceleration formula:
\[ a_c = \frac{(v)^2}{r} = \frac{\left(\frac{L}{T}\right)^2}{r} \]

4. **Expressing Radius in Terms of Dimensions**:
The radius \( r \) is also a length, so we can denote it as \( L \).

5. **Substituting Radius into the Formula**:
Now substituting \( r \) into the formula:
\[ a_c = \frac{\left(\frac{L}{T}\right)^2}{L} = \frac{\frac{L^2}{T^2}}{L} \]

6. **Simplifying the Expression**:
Simplifying the above expression gives:
\[ a_c = \frac{L^2}{T^2 \cdot L} = \frac{L}{T^2} \]

7. **Final Dimensions of Centripetal Acceleration**:
Therefore, the dimensions of centripetal acceleration are:
\[ [a_c] = [L][T^{-2}] \]

### Final Answer:
The dimensions of centripetal acceleration are \( [L][T^{-2}] \).