The pulley arrangements of figures (a) and (b) are identical. The mass of the rope is negligible. In Fig. (a), the mass m is lifted up by attaching a mass 2m to the other end of the rope. In Fig. (b) , m is lifted up by pulling the other end of the rope with a constant downward force F=2mg. The acceleration of m is the same in both cases.
True if m < 1 kg
In the first case, acceleration, a=(2m−m)gm+2m=g3
In the second case, acceleration, a′=F−mgm=2mg−mgm=g
Hence, the acceleration is different in both cases.