Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
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
⇒ 
……(iii)
⇒ 
= 2 m/s2
The acceleration of the masses is 2 m/s2
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.