Assuming mass mt moves down with an acceleration ‘a’
m1g -T = m1a1 ….. (1)
T – m2 g = m2 a1..…. (2)
(1) + (2)
m1g – m2g = (m1 + m2) a1
⇒ a1 = \((\frac {m_1-m_2}{m_1+m_2})g\)
& T = m1g – m1 \(((\frac {m_1-m_2}{m_1+m_2})g)\)
⇒ T = m1g \([1-\frac {m_1-m_2}{m_1+m_2}]\)
T = \(\frac {2m_1-m_2g}{m_1+m_2}\).