Check by dimensions whether the equation `tan theta=(rg)/(v^(2))` is correct.
Here, r = radius of curvature of path, g = acceleration due to gravity
v = velocity of body moving on the curved path, `theta`= angle of banking of the road

Answer

To check the dimensional correctness of the equation \( \tan \theta = \frac{rg}{v^2} \), we will analyze both sides of the equation step by step.

### Step 1: Analyze the Left-Hand Side (LHS)
The left-hand side of the equation is \( \tan \theta \). The tangent of an angle is a ratio of two lengths (opposite side over adjacent side), which means it is a dimensionless quantity.

**LHS:**
\[ \text{Dimension of LHS} = M^0 L^0 T^0 \]