m= 8 kg
M= 12 kg
g(acceleration due to gravity)=10 m/ s2
The system of masses and pulley has one smaller mass,’m’ and one larger mass, ‘M’.
‘T’ is the tension in the strings,
‘a’ is the acceleration of the masses.
The larger mass, ‘M’ moves downward with supposed acceleration ‘a’ and thus mass, ‘m’ moves upward.
According to the Newton’s second law of motion, we get equation of motion for each masses,
For mass m:
T – mg = ma …..(i)
For mass M:
Mg - T = Ma ……(ii)
We add both of the equation(i) and (ii), to get:
(M – m)g = (M+m)a
⇒ = 2 m/s2
The acceleration of the masses is 2 m/s2
To find tension, We substitute the value of a from eq(iii) in eq(ii), we get:
⇒ T=96 N
The tension in the string when the masses are released is 96 N.
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