For the lower part
Mass of the lower part is \(m^{\prime}=\) Mass per unit length \(\times\) length of lower part
\(=\frac{M}{L}(L-I)\)
So, Using \(\vec{F}_{\text {net }}=m \vec{a}\)
here \(\vec{a}=0\)
\(T-\frac{M}{L}(L-I) g=0\)
\(T=\frac{M}{L}(L-I) g\)