Check the dimensional correctness of the following equations :
(i) `T=Ksqrt((pr^3)/(S))` where p is the density, r is the radius and S is the surface tension and K is a dimensionless constant and T is the time period of oscillation.
(ii) `n=(1)/(2l)sqrt((T)/(m))`, when n is the frequency of vibration, l is the length of the string, T is the tension in the string and m is the mass per unit length.
(iii) `d=(mgl^3)/(4bd^(3)Y)`, where d is the depression produced in the bar, m is the mass of the bar, g is the accelaration due to gravity, l is the length of the bar, b is its breadth and d is its depth and Y is the Young's modulus of the material of the bar.

Explanation

To check the dimensional correctness of the given equations, we will analyze each equation step by step.

### (i) \( T = K \sqrt{\frac{pr^3}{S}} \)

1. **Identify the dimensions of each variable:**
- \( T \) (time period): \( [T] \)
- \( p \) (density): \( [M L^{-3}] \)
- \( r \) (radius): \( [L] \)
...