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

Explanation

Here, the pulling forec `F(=mg)` is same on both the wires, Let `Delta l_(1), Delta l_(2)` be the elongations in the two wires.
As, `Y=(Fl)/(pi r^(2) Delta l) or Delta l = (Fl)/(Y pi r^(2))`
For wire A, `Delta l_(1)=(mgl)/(Y pi r^(2))`
For wire B `Delta l_(2) = (mg (2l))/(Y pi (2r)^(2)) = (mgl)/(2 Y pi r^(2))`
Total elongation = `Delta l_(1)+Delta l_(2)`
`=(mgl)/(Y pi r^(2)) + 1/2 (mgl)/(Y pi r^(2)) = 3/2 (mgl)/(Y pi r^(2))`.