Time period 't' is a function of

1) L and 2) g

t= KL$^{a} .g^{b}$ (K=constant)

substituting the dimensions on both sides

T$^{\prime}=kL^{a}.(LT^{-2})^{b}$

equating the powers of M, L, and T on both sides we have

Power of T= 1= -2b

b=$\frac{-1}{2}$

Power of L, 0=a+b

a= - b

=$-(\frac{-1}{2})$

a=$\frac{1}{2}$

substituting the values of a and b in equation 1

t=KL$^{1/2}.g^{-1/2}$

k$\sqrt{\frac{L}{g}}$

The value of 'k' is determined from experiments which is

K=$2\pi$

t=2$\pi{\sqrt\frac{L}{g}}$