The length of metallic wire is l. The tensin in the wire is `T_(1)` for length ` l_(1)` and tension in the wire is `T_(2)` for length `l_(2).` Find the original length.

Explanation

Increase in length under tension `T_(1) = l _(1) - l`
Increase in length under tension `T_(2) =l_(2) -l`
`Y = (T_(1))/(A) xx (l )/( l _(1) - l) and Y = ( T_(2))/( A) xx (l)/(l _(2) -l)`
Since material of wire is same hence Y is same.
`therefore ( T_(1))/(A) xx ( l)/( l _(1) xx ) = (T_(2))/( A ) xx (l )/( l _(2) - l)`
`therefore T_(1) ( l _(2) - ) = T_(2) (l_(1) - l)`
`therefore T_(1) l _(2) -T_(1) l = T_(2) l _(1) - T_(2) l`
`therefore T_(1) l _(2) - T _(1) l _(1) = (T_(1) - T _(2)) l`
`therefore l = (T_(1) l_(2)- T_(2) l _(1))/( T_(1) - T_(2)) or (T _(2) l _(1) -T_(1) l _(2))/( T_(2)- T_(1))`