Check the correctness of the formula `f = (mv^2)/(r^2)` where f is force , m is mass , v is velocity and r is radius.

Explanation

To check the correctness of the formula \( f = \frac{mv^2}{r^2} \) using dimensional analysis, we will follow these steps:

### Step 1: Identify the dimensions of force
The left-hand side of the equation is force \( f \). The dimensional formula for force is given by:
\[ \text{Force} = \text{mass} \times \text{acceleration} \]
The dimensional formula for mass is \( [M] \) and for acceleration (which is \( \frac{\text{velocity}}{\text{time}^2} \)) is \( [L][T^{-2}] \). Therefore, the dimensional formula for force is:
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