Obtain an expression for the time period T of a simple pendulum. [The time period T depend upon (i) mass l of the bob (ii) length m of the pendulum and (iii) acceleration due to gravity g at the place where pendulum is suspended.
Assume the constant `k=2pi`]

Explanation

Here k is the dimensionless constant. Rewriting the above equation with dimensions.

Comparing the powers of M, L and T on both sides, a = 0, b + c= 0, -2c =1
Solving for a, b and `cimpliesa=0`, `b= 1 // 2`, and `c=-1 // 2`
From the above equation
`T=k m^(0)l^(1 // 2)g^(-1 // 2)`
`T=k((l)/(g))^(1 // 2) =ksqrt(l // g)`
Experimentally `k=2pi`, hence
`T=2pisqrt(l // g)`