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A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)
- a)68 cm
- b)6.8 cm
- c)113.9 cm
- d)88 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A copper rod of 88 cm and an aluminium rod of an unknown length have ...
When the temperature is increased by ΔT, their final lengths,
As change in lengths are equal, LCu − L1 = LAl − L2
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Community Answer
A copper rod of 88 cm and an aluminium rod of an unknown length have ...
Given data:
Length of copper rod, Lcopper = 88 cm
Coefficient of linear expansion of copper, αcopper = 1.7 × 10-5 K-1
Coefficient of linear expansion of aluminum, αaluminum = 2.2 × 10-5 K-1
Let's assume the increase in temperature is ΔT for both the copper and aluminum rods.
Since both rods have an equal increase in their lengths, we can equate the change in lengths of the two rods.
Change in length of copper rod = αcopper * Lcopper * ΔT
Change in length of aluminum rod = αaluminum * Laluminum * ΔT
Since the change in length is equal for both rods, we can write:
αcopper * Lcopper * ΔT = αaluminum * Laluminum * ΔT
Cancelling ΔT from both sides, we get:
αcopper * Lcopper = αaluminum * Laluminum
Now, substituting the given values:
(1.7 × 10-5 K-1) * 88 cm = (2.2 × 10-5 K-1) * Laluminum
Simplifying the equation:
Laluminum = (1.7 × 10-5 K-1 * 88 cm) / (2.2 × 10-5 K-1)
Laluminum = (1.7 * 88) / 2.2 = 68 cm
Therefore, the length of the aluminum rod is 68 cm. Hence, option A is the correct answer.
Length of copper rod, Lcopper = 88 cm
Coefficient of linear expansion of copper, αcopper = 1.7 × 10-5 K-1
Coefficient of linear expansion of aluminum, αaluminum = 2.2 × 10-5 K-1
Let's assume the increase in temperature is ΔT for both the copper and aluminum rods.
Since both rods have an equal increase in their lengths, we can equate the change in lengths of the two rods.
Change in length of copper rod = αcopper * Lcopper * ΔT
Change in length of aluminum rod = αaluminum * Laluminum * ΔT
Since the change in length is equal for both rods, we can write:
αcopper * Lcopper * ΔT = αaluminum * Laluminum * ΔT
Cancelling ΔT from both sides, we get:
αcopper * Lcopper = αaluminum * Laluminum
Now, substituting the given values:
(1.7 × 10-5 K-1) * 88 cm = (2.2 × 10-5 K-1) * Laluminum
Simplifying the equation:
Laluminum = (1.7 × 10-5 K-1 * 88 cm) / (2.2 × 10-5 K-1)
Laluminum = (1.7 * 88) / 2.2 = 68 cm
Therefore, the length of the aluminum rod is 68 cm. Hence, option A is the correct answer.
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A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer?
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A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer?.
A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A copper rod of 88 cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is : (αCu = 1.7 × 10-5K-1 and αAl = 2.2 × 10−5 K−1)a)68 cmb)6.8 cmc)113.9 cmd)88 cmCorrect answer is option 'A'. Can you explain this answer?.
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