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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Similar questions

Q. 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 lengths of steel and copper rods are so that the length of the steel rod is 5 cm longer than that of the copper rod at all temperatures, then length of each rod, are ( $α$ for copper = $1.7 \times 10^{- 5} /^{\circ} C$ and $α$ for steel = $1.1 \times 10^{- 5} /^{\circ} C$ ) -

Three aluminium rods of equal length form an equilateral triangle $A B C$ . Take $O$ (mid point of rod $B C$ ) as the origin. The increase in Y-coordinate of center of mass per unit change in temperature of the system is given as $x \times 10^{- 6} m /^{\circ} C$ . Find $x$ . Assume the length of each rod is $2 m$ , and $α_{a l} = 4 \sqrt{3} \times 10^{- 6} /^{\circ} C$ .

Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are $12 \times 10^{- 6}^{\circ} C^{- 1}$ and $23 \times 10^{- 6}^{\circ} C^{- 1}$ respectively.

Q. What should be lengths of steel and copper rod, so that the length of steel rod is

5 c m

longer than the copper rod at all temperatures? (

α

of copper

- 1.7 \times 10^{- 5}^{o} C^{- 1}

and

α

for steel

= 1.1 \times 10^{- 5}^{o} C^{- 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,
${(Δ l)}_{C u} = {(Δ l)}_{A l} l_{C u} α_{C u} Δ T = l_{A l} α_{A l} Δ T 88 \times 1.7 \times 10^{- 5} = l_{2} \times 2.2 \times 10^{- 5} l_{A l} = 68 c m$