The length of a metal wire is l1 when the tension in it is T1 and is

1.	The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T, The natural length of the wire is(a) (l1+l2)/2(b) √(l1l2)(c) (l1T2-l2 T1)/(T2-T1)(d) (l1T2+l2T1)/(T2+T1)
Answer» (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 = T₁l/Ya And l₂-l = T₂l/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).

The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T, The natural length of the wire is(a) (l1+l2)/2(b) √(l1l2)(c) (l1T2-l2 T1)/(T2-T1)(d) (l1T2+l2T1)/(T2+T1)

Answer»

(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).