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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 as shown in figure. The net elongation is


  1. 2mgl3πr2Y
  2. 3mglπr2Y
  3. 3mgl4πr2Y
  4. 3mgl2πr2Y


Solution

The correct option is D 3mgl2πr2Y

Tension in both wires will be same.

Let elongation in wire 1 be =Δl1
Δl1=mglπr2Y        [Δl=FlAY]
[A=πr2]
Let elongation in wire 2 be =Δl2
Δl2=mg×(2l)π(2r)2Y=mgl2πr2Y
[ given length of wire 2 =2l, radius of wire 2=2r]
So, net elongation
(Δl)net=Δl1+Δl2=mglπr2Y+mgl2πr2Y
Δlnet=3mgl2πr2Y

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