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A wire elongates by l mm when a load W is hanged from it.If the wire goes over a pulley and two weights W each are hung at the two ends,the elongation of the wire will be(in mm)
We know that the Young’s modulus Y = Force x L / A x l Or rewriting we have Y = WL/Al \ l= WL/ AY Since the length of the wire is on both sides of the pulley length L/2 will be on both sides. Thus the elongation of the wire in mm is l mm. Thanks & Regards, Vasantha Sivaraj, askIITians faculty
We know that the Young’s modulus Y = Force x L / A x l
Or rewriting we have Y = WL/Al
\ l= WL/ AY
Since the length of the wire is on both sides of the pulley length L/2 will be on both sides.
Thus the elongation of the wire in mm is l mm.
Thanks & Regards,
Vasantha Sivaraj,
askIITians faculty
Dear student,Please find the attached solution to your question. We know ΔL = FL/AY In first case, ΔL1 = WL/AY = l mmIn second case, ΔL2 = 2 x W*0.5L/AY = WL/AY (Area of cross section is the same, while youngs modulus being the property of material is unchanged)Hence, ΔL2 = ΔL1 = l mm Hope it helps.Thanks and regards,Kushagra
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