Question:
A composite wire is made by joining ends of two wire of equal dimensions.One of copper and the other of steel.When a weight is attached to its end the ratio of increases in their lengths is?(Ysteel = 20/7 Ycopper)
Answer:
We know that Youngs modulus is Y = (F/A) / ∆l /l
For steel, Y1 = (F/A1) / ∆l1 /l1
For copper, Y2 = (F/A2) / ∆l2 /l2
Given that the dimensions of the steel and copper wire are same. Hence, A1 = A2 and l1 = l2
Y1 / Y2 = ∆l2 / ∆l1
Given Y1 = 7/20 Y2, implies = ∆l2 / ∆l1 equals to 7/20
Increase in length ratio between steel and copper is ∆l1 / ∆l2 20/7
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