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T - m1g = m1a ...........1
m2g - T = m2a ...........2 (m2 > m1 )
adding both
a = (m2-m1)g/(m1+m2) .............3
now , m1 will move upward but m2 will move downward ...
accleration of m1 is a1 = a(j) (upward is taken as +ve)
accleration of m2 is a2 = a(-j) (downward is taken as -ve)
accleration of center of mass is acom = m1a1 + m2a2 /m1+m2
acom = (m1a - m2a)/m1+m2 (j)
substituting a from eq 3
acom = -g(m2-m1)2/(m1+m2)2 (j)
accleration of com will be in downward direction
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