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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)

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)

Grade:12

2 Answers

Vasantha Kumari
askIITians Faculty 38 Points
10 years ago

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

181-362_Youngs mod.JPG
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your question.
 
We know ΔL = FL/AY
In first case, ΔL1 = WL/AY = l mm
In 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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