The length of a steel wire is `l_(1)` when the stretching force is `T_(1)` and `l_(2)` when the stretching force is `T_(2)`. The natural length of the wire is

Options

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

`Y=(Fl)/(a/_\l)`
`Y, l` and `a` are consants
`:. (Fl)/(/_\l)=` constant or `/_\lpropF`
Now, `l_(1)-l=T_(1)` and `l_(2)-l=T_(2)`
Dividng `(l_(1)-l)/(l_(2)-l)=(T_(1))/(T_(2))`
or `l_(1)T_(2)-lT_(2)=l_(2)T_(1)=lT_(1)` or `T(T_(1)-T_(2))=l_(2)T_(1)-l_(1)T_(2)`
or `l=(l_(2)T_(1)-l_(1)T_(2))/(T_(1)-T_(2))` or `l=(l_(1)T_(2)-l_(2)T_(1))/(T_(3)-T_(1))`