$(20$ points$)$ For the two$-$cell section, assuming shear modulus $G=27$GPa. please $($ a $)$ express the torque $T$ in terms of $q_1$ and $q_2,(b)$ if the twist angle $=2\frac{}{m},$ find the values of $q_1$ and $q_2,(c)$ determine the applied torque $T,$ and $(d)$ find the torsional rigidity of the two$-$cell section.

$t_1=0\mathrm{.}1cm=1{10}^{-3}m$

$t_2=0\mathrm{.}3cm=3{10}^{-3}m$

$t_{12}=0\mathrm{.}2cm=2{10}^{-3}m$

$15$