Two wires A and B of length l, radius r and length 2l, radius 2r having same Young's modulus Y are hung with a weight mg. What is the net elongation in the two wires?

Explanation

Here, the pulling force, `F(=mg)` is same on both the wires. Let `Deltal_(1),Deltal_(2)` be the elongations in the two wires.

As, `Y=(Fl)/(pir^(2)Deltal)`
(or) `Deltal=(Fl)/(Ypir^2)`
For wire A, `Deltal_(1)=(mgl)/(Ypir^2)`
For wire B, `Deltal_(2)=(mg(2l))/(Ypi(2r)^(2))=(mgl)/(2Ypir^2)`
Total elongation `=Deltal_(1)+Deltal_(2)`
`=(mgl)/(Ypir^2)+(1)/(2)(mgl)/(Ypir^2)`
`=(3)/(2)(mgl)/(Ypir^2)`