A wire of length `L` and radius `r` is fixed at one end. When a stretching force `F` is applied at free end, the elongation in the wire is `l`. When another wire of same material but of length `2L` and radius `2r`, also fixed at one end is stretched by a force `2F` applied at free end, then elongation in the second wire will be

Options

A. `(l)/(2)`
B. `l`
C. `2l`
D. `4l`

Answer

B

Explanation

Both the wires are of same material, so Young's modulus will be same
`Y = (f)/(pi r^(2)) xx (L)/(l) = (2f)/(pi (2r)^(2)) xx (2L)/(x)`
`x = l`