An Iron rod and a copper rod lie side by side. As the temperature is changed, the difference in the lengths of the rods remains constant at a value of 10 cm. Find the lengths at 0∘C. Coefficients of linear expansion of iron and copper are 1.1 × 10−6/∘C and 1.7 × 10−5/∘C respectively.
An Iron rod and a copper rod lie side by side. As the temperature is changed, the difference in the lengths of the rods remains constant at a value of 10 cm. Find the lengths at 0∘C. Coefficients of linear expansion of iron and copper are 1.1 × 10−6/∘C and 1.7 × 10−5/∘C respectively.
The correct option is A 28.3 cm, 18.3 cm
Iiθ = Ii0(1 + \alpha_{i}\theta)\) .....................(1)
and Icθ = Ic0(1+αcθ). ......................(2)
Subtracting,
Iiθ−Icθ = (Ii0−Ic0)+(Ii0αi−Ic0αc)θ. ............(3)
Now,
Iiθ−Icθ = Ii0−Ic0 (= 10 cm).
Thus, from (3),
Ii0αi = Ic0αc
or, li0lc0 = αcαi
or, li0li0−lc0 = αcαc−αi
= 1.7 × 10−5/∘C0.6 × 10−5/∘C = 176.
This shows that [Ii0−Ic0] is positive. Its value is 10 cm as given in the question.
Hence, Ii0 = 176 × (Ii0−Ic0)
= 176 × 10 cm = 28.3 cm
and Ic0 = Ii0−10 cm = 18.3 cm
28.3 cm, 18.3 cm
Iiθ = Ii0(1 + \alpha_{i}\theta)\) .....................(1)
and Icθ = Ic0(1+αcθ). ......................(2)
Subtracting,
Iiθ−Icθ = (Ii0−Ic0)+(Ii0αi−Ic0αc)θ. ............(3)
Now,
Iiθ−Icθ = Ii0−Ic0 (= 10 cm).
Thus, from (3),
Ii0αi = Ic0αc
or, li0lc0 = αcαi
or, li0li0−lc0 = αcαc−αi
= 1.7 × 10−5/∘C0.6 × 10−5/∘C = 176.
This shows that [Ii0−Ic0] is positive. Its value is 10 cm as given in the question.
Hence, Ii0 = 176 × (Ii0−Ic0)
= 176 × 10 cm = 28.3 cm
and Ic0 = Ii0−10 cm = 18.3 cm
