The length of a metal wire is `l_(1)` when the tension in it is `T_(1)` and is `l_(2)` when the tension is `T_(2)`. Then natural length of the wire is

Options

A. `((l_(1)+l_(2)))/(2)`
B. `((l_(1)-l_(2)))/(2)`
C. `(l_(1)T_(2)-l_(2)T_(1))/(T_(2)-T_(1))`
D. `(l_(1)T_(2)+l_(2)T_(1))/(T_(2)+T_(1))`

Answer

C

Explanation

When tension `T_(1)` is applied its length elongate to `l_(1)`,
`therefore x=l_(1)-L`, When `T_(1)` is
`y=l_(2)-L`, when applied tension `T_(2)` is applied.
`T_(1) prop x and T_(2) prop x`
`(T_(1))/(T_(2))=(x)/(y)=(l_(1)-L)/(l_(2)-L)`
`T_(1)(l_(2)-L)=T_(2)(l_(1)-L)`
`T_(1)l_(2)-LT_(1)=T_(2)l_(1)-LT_(2)`
`L[T_(2)-T_(1)] = T_(2)l_(1)-T_(1)l_(2)`
`therefore L=(T_(2)l_(1)-T_(1)l_(2))/(T_(2)-T_(1))`