Let's discuss a beautiful problem useful for Physics Olympiad based on masses over a frictionless pulley.
The Problem: Masses over a frictionless pulley
Two bodies A and B hanging in the air are tied to the ends of a string which passes over a frictionless pulley. The masses of the string and the pulley are negligible and the masses of two bodies are 2kg and 3kg respectively. (Assume g=(10m/s^2)). Body A moves upwards under a force equal to
(a)30N
(b)24N
(c)10N
(d)4N
Solution:
The masses of two bodies are 2kg and 3kg respectively. The acceleration of A is
$$ a=\frac{3-2}{3+2}g=2m/s^2$$
The net force on A will be F=ma=(2\times2)=4N.
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