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Standard XII

Physics

Thermal Expansion

A copper rod ...

Question

A copper rod and a steel rod maintain a difference in their lengths constant= 10 cm at all temperatures. If their coefficients of expansion are $1.6 \times 10^{- 5} K^{- 1}$ and $1.2 \times 10^{- 5} K^{- 1}$ , then the length of the Cu rod is

40 cm

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30 cm

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32 cm

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24 cm

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Solution

The correct option is A 30 cm
Let $l_{1}$ be the length of Cu and that of steel be $l_{2}$ .
As the difference in their lengths is constant, thus
$(l_{2} - l_{1}) = (l_{2} + l_{2} α_{2} - l_{1} - l_{2} α_{1}) Δ T$
$l_{2} α_{2} - l_{1} α_{1} = 0$
$\frac{l_{2}}{l_{1}} = \frac{α_{1}}{α_{2}}$
$\frac{l_{2}}{l_{1}} - 1 = \frac{α_{1}}{α_{2}} - 1$
$\frac{l_{2} - l_{1}}{l_{1}} = \frac{α_{1} - α_{2}}{α_{2}}$
$\frac{10}{l_{1}} = \frac{0.4}{1.2}$
$l_{1} = 30 c m$

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A copper rod and a steel rod maintain a difference in their lengths constant= 10 cm at all temperatures. If their coefficients of expansion are 1.6×10−5K−1 and 1.2×10−5K−1, then the length of the Cu rod is

The correct option is A 30 cmLet l1 be the length of Cu and that of steel be l2.As the difference in their lengths is constant, thus(l2−l1)=(l2+l2α2−l1−l2α1)ΔTl2α2−l1α1=0l2l1=α1α2l2l1−1=α1α2−1l2−l1l1=α1−α2α210l1=0.41.2l1=30cm

A copper rod and a steel rod maintain a difference in their lengths constant= 10 cm at all temperatures. If their coefficients of expansion are $1.6 \times 10^{- 5} K^{- 1}$ and $1.2 \times 10^{- 5} K^{- 1}$ , then the length of the Cu rod is