According to the question,
m1 = 8 kg
m2 = 12 kg
Tension = T
The heavier mass m2 will move downwards and the smaller mass m1 will move upwards.
On Applying Newton’s second law,
For mass m1:
T – m1g = m1a —– (1)
For mass m2:
m2g – T = m2a ——(2)
Add (1) and (2)
(m2 – m1) g = (m1 + m2) a
a = (m2 – m1) g/ (m1 + m2)
=[ (12 – 8)/(12 + 8)] x 10 = (4 /20) x 10= 2m/s
Therefore, acceleration of the mass is 2 m/s2
m2g – T = m2a
m2g – T = m2 [ (m2 – m1) g/ (m1 + m2) ]
= 2m1m2g/(m1 + m2)
T = 2 x 12 x 8 x 10/ (12 + 8)
T = 96 N
Hence, the tension on the string is 96 N