Question

The length of a metal wire is l₁ when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is

(a) (l₁ = l₂)/2

(b) √(l₁l₂)

(c) (l₁T₂ - l₂T₁)/(T₂ - T₁)

(d) (l₁T₂ + l₂T₁)/(T₂ + T₁).

Answer 1

(c) (l₁T₂-l₂ T₁)/(T₂-T₁)

Explanation: 

If the original length of the wire be l and the area of the cross-section a, then  

l₁-l = T₁*l/Ya 

And l₂-l = T₂*l/Ya 

Dividing we get, 

(l₁ -l)*T₂ = (l₂-l)*T₁ 

→l₁T₂ -lT₂= l₂ T₁-T₁l 

→l(T₂-T₁) = l₁T₂-l₂T₁

 →l = (l₁T₂-l₂T₁)/(T₂-T₁) 

Hence the option (c).