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If a mass is suspended from the ceiling by a massless rope, will tension be the same at all points on the rope?

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Let's assume that tension increases down the rope then for this section of rope to be in equilibrium $$T-(T+\Delta T)=\Delta mg$$

As rope is massless, $\Delta m=0$

So, $\Delta T=0$

Therefore the magnitude of tension is constant throughout the massless rope.

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Yes, otherwise rope will be break , also $F_{net}$ on the rope wont be 0.

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A massless rope isn't a real thing. It is an idealization to make problems in first physics courses easier. This is done so you can learn about how objects accelerate when they exert forces on each other without extra complications from the rope. So yes, this ideal rope will have the same tension everywhere. It won't stretch, or break, or do other things a real rope might do.

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