In a pulley system, why is the tension force the same for both objects?

 

Let us consider that the tension is not equal, as per the Newton's law of motion, the expression of the motion is given as:

ma=T₁−T₂-mg

m= mass of the rope, which is ideally zero.

Hence, the above expression becomes,

0=T₁−T₂

T₁=T₂=T

The rope is always considered to be massless, hence the tension is same on both the side.

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