Question

The length of a metal wire is l1 when the tension in it is T1and 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).