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`
B. `2l`
C. `l//2`
D. `4l`

Answer

A

Explanation

`y=(F_(1)L_(1))/(pi r_(1)^(2)l_(1)) " " therefore l_(1)=(ypi r_(1)^(2))/(F_(1)L_(1))`
`y=(F_(2)L_(2))/(pi r_(2)^(2)l_(2))" " therefore l_(2)=(y pi r_(2)^(2))/(F_(2)L_(2))`
`therefore (l_(2))/(l_(1))=(r_(2)^(2))/(r_(1)^(2)) xx (L_(1))/(L_(2)) xx (F_(1))/(F_(2))`