Why do the pulleys in parallegrom law of vector addition need to be frictionless?
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You need to understand the fact that if the pulleys were having friction in them, then they would have rotated during movement of the strings on them.
In that case you also need to consider rotational mechanics of the pulley and the strings on either side of pulley will have different tension.
In order to make the problem simple, the pulleys are called frictionless.
In rotational mechanics chapter class 11, you will have frictional pulley, then you will understand more clearly.
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