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, The natural length of the wire is

Monjur Alahi

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)


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Salim Ahmed Kawsar

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(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).

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