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Q.

Two wires of length l , radius r and length 2l , radius 2r respectively having same Young’s modulus are hung with a weight mg . Net elongation is

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a

3mgl2πr2Y

b

3mgl4πr2Y

c

3mglπr2Y

d

2mgl3πr2Y

answer is C.

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Detailed Solution

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Young's modulus

 Y=mgla1l1l1=mglYπr2 ..(1) and  Y=mg(2l)a2l2=mg(2l)π(2r)2l2 or l2=mgl2Yπr2..(2) 

From Eqs. (1) and (2), we have 

 l1+l2=mglYπr2+mgl2Yπr2=32mglYπr2

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Two wires of length l , radius r and length 2l , radius 2r respectively having same Young’s modulus are hung with a weight mg . Net elongation is