If all the pulleys are connected with the same string why is tension same at all points? Shouldn't $T_2 =2T$ and $T_3=2T_2$?
closed as off-topic by Hritik Narayan, Yashas, Jon Custer, sammy gerbil, David Hammen Jun 26 '17 at 12:28
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Your remark "same string" says it all. It's a freely moving string (despite any intricacies of stuff its wrapped around) -- so tension at any point must equal tension at any other.
But here's another way to look at it. And, as is often the case in mechanical situations, "another way" involves energy. Since it's the "same string", suppose you grab it at some (any) point and pull it one foot. Then every other point on the string also moves that exact same one-foot distance. So force$\equiv$tension $\times$ distance is the work/energy involved. Now, if $T$ were different anywhere along the string, apply work to pull it at the small-$T$ point, and extract work at the large-$T$ point. Bingo! You've got more energy out than you put in, and the world's energy crisis is history.