Answer
$T_2 = 55.1~N$
Work Step by Step
In part (a), we found that $~~\alpha = 31.4~rad/s^2$
In part (c), we found that $T_1 = 56.1~N$
Since we don't know if there is friction between the block and the horizontal surface, we can use the torque and the pulley to find $T_2$:
$\sum~\tau = I~\alpha$
$R~T_1-R~T_2 = I~\alpha$
$R~T_2 = R~T_1-I~\alpha$
$T_2 = T_1-\frac{I~\alpha}{R}$
$T_2 = (56.1~N)-\frac{(7.40\times 10^{-4}~kg~m^2)(31.4~rad/s^2)}{0.0240~m}$
$T_2 = 55.1~N$
