Question

find the dimensions of I

Answer 1

The physical quantities can be added only when they have same dimensions. In the given expression of the time period we have a term:
$\frac{l}{r^2} +m$
It means that the term "$\frac{l}{r^2}$" must have a dimension of mass.
In dimensional formula, 
$\frac{[l]}{[r^2]} =M \\ Now, [r^2]=L^2 \\ Therefore, [l]=ML^2$