When a weight `W` is hung from one end of a wire of length `L` (other end being fixed), the length of the wire increases by `l`. If the same wire is passed over a pulley and two weights `W` each are hung at the two ends,what will be the total elongation in the wire?
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In case a let `Y` be Young's modulus of the material of the wire. If a is its area of cross section, then we can write `y=(F//aF//a)/(l//L l//L)=(WL)/(al)(:'F=W)` Increase in length of wire `l=(WL)/(aY)` In case b we can treat either segment of length `L//2` in fig. as if one to its ends is ficed while the other end is attached to the load `W` because the point `M` remains stationary i.e., fixed all the time due to symmetrical load. Thus, when the wire is passed over the pulley, let `l'` be the increase in the length of each segment. Since each segment is of length `L//2`, we have `Y=(W(L//2))/(al')` Increase in length of wire of one side of pulley `l'=1/2 (WL)/(aY)=l/2` Therefore, increase in the length of both segments of the wire `=l'+l'=l/2+l/2=l` so the increase in length remains the same.
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