The time period T of simple pendulum depends upon length l of the pendulum and gravitational acceleration. The formula for time period of simple pendulum is given by

Let T∝la     and   T∝gbwhere a and b are dimensionless constantsT=klagbwhere, k is dimensionless constant.[LHS][T]=[M0L0T−1]and [RHS](lagb)=[L]a[LT−2]b=[La+bT−2b]=[M0La+bT−2b]According to homogeneity principle,[LHS] = [RHS]or [M0L0T]=[M0La+bT−2b]For dimensional balance, dimensions on both sides should be same.∴   a+b=0and -2b =1∴           b=−12and a=12∴       T=2πlg[since, numerical value of k in case of simple pendulum is 2π]