The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and radius ( r) of the circle . Derive the formula for F using the method of dimensions.

Explanation

To derive the formula for the centripetal force \( F \) acting on a particle moving uniformly in a circle using the method of dimensions, we can follow these steps:

### Step 1: Identify the Variables
We know that the centripetal force \( F \) may depend on the mass \( m \), velocity \( v \), and radius \( r \) of the circle. We can express this relationship as:
\[ F = k \cdot m^a \cdot v^b \cdot r^c \]
where \( k \) is a dimensionless constant, and \( a \), \( b \), and \( c \) are the powers we need to determine.
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