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. The natural length of the wire is?

Correct option is B. l1T2−l2T1/T2−T1
Let l = original length of the wire.
A = original area of the metal wire.
Change in length in first case = l1−l
Change in length in second case = l2−l
Young Modulus = Normal Stress / Longitudinal strain
Y = T A / (Δl/l)
where Y = Young Modulus
T = Tension
A = Area
Δl = Change in Length
l = Original length
In First Case
Y = T1A / (l1−l)
In Second case :
Y = T2A / (l2−l)
Since Young Modulus remains the same
So, T1A / (l1−l) = T2A / (l2−l)
On solving we get
l = l1T2−l2T1 / T2−T1