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

The length of metallic wire is l. The tensin in the wire is T_(1) for

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