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. `sqrt(l_(1)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_(1)+T_(2))`

Answer

C

Explanation

(c) As, Young's modulus of elasticity , `Y=("Stress")/("Strain")`
`implies Y=(T_(1)xxL)/(Axx(l_(1)-L))" "…(i)`
where, L is the original length of the wire and also
`Y=(T_(2)xxL)/(Axx(l_(2)-L))" "(ii)`
From Eqs. (i) and (ii) , we get
`(T_(1)L)/(A(l_(1)-L))=(T_(2)L)/(A(l_(2)-L))implies L=(T_(2)l_(1)-T_(1)l_(2))/(T_(2)-T_(1))`