Answer
$T_2 = 4.94~N$
Work Step by Step
In part (a), we found that $a = 1.57~m/s^2$
We can consider the forces on $m_2$ to find $T_2$:
$ m_2~g-T_2 = m_2~a$
$T_2 = m_2~(g-a)$
$T_2 = (0.600~kg)~(9.8~m/s^2-1.57~m/s^2)$
$T_2 = 4.94~N$
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