Tension in a massless string

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Why is tension in a massless string same throughout its length?
 

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Why is tension in a massless string same throughout its length?

Consider a massless string being pulled horizontally towards right.

The forces acting on a tiny bit of the string having mass Δm will be T1 towards right and T2 towards left.The force equation will be T2-T1=Δma where 'a' is the acceleration of the tiny bit of the string .Now since Δm=0 ∴ T2=T1 i.e tension on either side of any arbitrary mass of the string is zero.In other words tension throughout the string is constant.
 

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