Fig shows a wire of length landof slightly non-uniform cross-section. Its radius at one end is `R_(1)`, and at the other, it is `R_(2)` .

The wire is stretched by forces Fand F applied along the length in opposite directions and normal to the ends Y being the Young's modulus, extension caused in the wire is nearly:

Options

A. `(Fl)/(pi Y R_(1) R_(2))`
B. `(FlY)/(R_(1)R_(2)) `
C. `(FlY)/(pi R_(1)^(2) R_(2)^(2))`
D. `(FY)/(l pi R_(1) R_(2))`

Answer

A

Explanation

`F = (Y A Deltal)/(l) :. Deltal = (Fl)/(YA) "or" Deltal = (Fl)/(Ysqrt(A_(1)A_(2)))=(Fl)/(Ysqrt(piR_(1)^(2)piR_(2)^(2)))=(Fl)/(Y pi R_(1)R_(2))`