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Mechanics
TENSION IN THE ROPE .
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WHY TENSION IN A STRING ACTS IN A DIRECTION OPPOSITE TO THE OBJECT TO WHICH IT IS ATTACHED WHEN WE MAKE FBD's .












Thats obvious because the string is inelastic (its length is always constant) so every little part of the string pulls the adjacent little part of the string with a force of the same magnitude (say dT) so that the string doesn't change in its physical dimension (to keep its length constant). Hence the direction of tension is always opposite to the force that is applied at its end, so that the length of the string remains same.