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A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-
(1) area of one face of the cube?
(2) volume of the cube?
(1) area of one face of the cube?
(2) volume of the cube?
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A thin copper wire of length L increases in length by 2% when heated f...
Problem: A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:
(1) area of one face of the cube?
(2) volume of the cube? Explain in details.
Solution:
Given, the thin copper wire increases in length by 2% when heated from T1 to T2.
Percentage change in length of wire: 2%
Let's calculate the new length of the wire.
New length = Initial length + Increase in length
= L + 0.02L
= 1.02L
Now, let's calculate the increase in dimensions of the copper cube.
(1) Percentage change in area of one face of the cube:
Initial area of one face of the cube = 10L x 10L = 100L^2
New area of one face of the cube = (1.02L) x (1.02L) = 1.0404L^2
Increase in area of one face of the cube = New area - Initial area
= 1.0404L^2 - 100L^2
= -98.9596L^2
Percentage change in area of one face of the cube = (Increase in area / Initial area) x 100%
= (-98.9596L^2 / 100L^2) x 100%
= -98.9596%
Therefore, the area of one face of the copper cube decreases by 98.9596%.
(2) Percentage change in volume of the cube:
Initial volume of the cube = 10L x 10L x 10L = 1000L^3
New volume of the cube = (1.02L) x (1.02L) x (1.02L) = 1.061208L^3
Increase in volume of the cube = New volume - Initial volume
= 1.061208L^3 - 1000L^3
= 61.208L^3
Percentage change in volume of the cube = (Increase in volume / Initial volume) x 100%
= (61.208L^3 / 1000L^3) x 100%
= 6.1208%
Therefore, the volume of the copper cube increases by 6.1208%.
Conclusion:
When a copper cube having side 10L is heated from T1 to T2, the area of one face of the cube decreases by 98.9596% and the volume of the cube increases by 6.1208%.
(1) area of one face of the cube?
(2) volume of the cube? Explain in details.
Solution:
Given, the thin copper wire increases in length by 2% when heated from T1 to T2.
Percentage change in length of wire: 2%
Let's calculate the new length of the wire.
New length = Initial length + Increase in length
= L + 0.02L
= 1.02L
Now, let's calculate the increase in dimensions of the copper cube.
(1) Percentage change in area of one face of the cube:
Initial area of one face of the cube = 10L x 10L = 100L^2
New area of one face of the cube = (1.02L) x (1.02L) = 1.0404L^2
Increase in area of one face of the cube = New area - Initial area
= 1.0404L^2 - 100L^2
= -98.9596L^2
Percentage change in area of one face of the cube = (Increase in area / Initial area) x 100%
= (-98.9596L^2 / 100L^2) x 100%
= -98.9596%
Therefore, the area of one face of the copper cube decreases by 98.9596%.
(2) Percentage change in volume of the cube:
Initial volume of the cube = 10L x 10L x 10L = 1000L^3
New volume of the cube = (1.02L) x (1.02L) x (1.02L) = 1.061208L^3
Increase in volume of the cube = New volume - Initial volume
= 1.061208L^3 - 1000L^3
= 61.208L^3
Percentage change in volume of the cube = (Increase in volume / Initial volume) x 100%
= (61.208L^3 / 1000L^3) x 100%
= 6.1208%
Therefore, the volume of the copper cube increases by 6.1208%.
Conclusion:
When a copper cube having side 10L is heated from T1 to T2, the area of one face of the cube decreases by 98.9596% and the volume of the cube increases by 6.1208%.
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A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube?
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A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube?.
A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin copper wire of length L increases in length by 2% when heated from T1 to T2. If a copper cube having side 10L is heated from T1 to T2 what will be the percentage change in:-(1) area of one face of the cube?(2) volume of the cube?.
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