A copper rod of length $88 c m$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is
( $α_{C u} = 1.7 \times 10^{- 5} K^{- 1}$ and $α_{A l} = 2.2 \times 10^{- 5} K^{- 1}$ )

6.8 c m

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113.9 c m

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88 c m

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68 c m

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Solution

The correct option is D $68 c m$
Since, the elongation is same for both the rods,
${(Δ l)}_{C u} = {(Δ l)}_{A l} l_{C u} α_{C u} Δ T = l_{A l} α_{A l} Δ T 88 \times 1.7 \times 10^{- 5} = l_{2} \times 2.2 \times 10^{- 5} l_{A l} = 68 c m$

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88 c m

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α_{C u} = 1.7 \times 10^{- 5} K^{- 1}

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α_{A l} = 2.2 \times 10^{- 5} K^{- 1}

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A copper rod of length 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is (αCu = 1.7×10−5 K−1 and αAl = 2.2×10−5 K−1)

The correct option is D 68 cmSince, the elongation is same for both the rods, (Δl)Cu = (Δl)AllCuαCuΔT = lAlαAlΔT88×1.7×10−5 =l2×2.2×10−5lAl = 68 cm

A copper rod of length $88 c m$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of the aluminium rod is
( $α_{C u} = 1.7 \times 10^{- 5} K^{- 1}$ and $α_{A l} = 2.2 \times 10^{- 5} K^{- 1}$ )

The correct option is D $68 c m$
Since, the elongation is same for both the rods,
${(Δ l)}_{C u} = {(Δ l)}_{A l} l_{C u} α_{C u} Δ T = l_{A l} α_{A l} Δ T 88 \times 1.7 \times 10^{- 5} = l_{2} \times 2.2 \times 10^{- 5} l_{A l} = 68 c m$