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You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?
- a)0.36 mm
- b)0.34 mm
- c)0.38 mm
- d)0.40 mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
You hang a flood lamp from the end of a vertical steel wire. The flood...
F/A = e/L
F/A = 0.18/l ( let the length be l)
F/A = x/2l
0.18/L = x/2l
0.18×2l = xl
0.36l = xl
x = 0.36
F/A = 0.18/l ( let the length be l)
F/A = x/2l
0.18/L = x/2l
0.18×2l = xl
0.36l = xl
x = 0.36
Most Upvoted Answer
You hang a flood lamp from the end of a vertical steel wire. The flood...
Given: The flood lamp stretches the wire by 0.18 mm, and stress is proportional to strain.
To find: How much would the wire stretch if it were twice as long.
Solution:
Let us assume the original length of the wire as L and the elongation produced by the flood lamp as δL.
According to Hooke's law, stress is proportional to strain.
Hence, Stress/Strain = Constant (K)
Let us assume the constant K as k.
Therefore, Stress = k × Strain
The strain is given by the formula,
Strain (ε) = δL/L
Stress (σ) = F/A
where F is the force applied, and A is the cross-sectional area of the wire.
As the wire is hanging vertically, the force acting on the wire is its weight, which is given by:
F = mg
where m is the mass of the lamp, and g is the acceleration due to gravity.
Hence, the strain can be calculated as follows:
Strain (ε) = δL/L = σ/k
σ = F/A = mg/A
Thus, we have:
δL/L = σ/k = (mg/A)/k
δL = (mgL/kA)
As the stress is proportional to strain, we can write:
δL/L = K1
where K1 is the constant of proportionality.
Thus, we have:
K1 = δL/L = (mgL/kA)
Now, we need to find the elongation produced when the length of the wire is doubled.
Let the new length of the wire be 2L.
The new cross-sectional area of the wire is the same as the original one.
Hence, the new elongation produced can be calculated as follows:
δL' = K1 × 2L = 2K1L
δL' = 2(δL/L)L
δL' = 2(0.18mm/1m)1m
δL' = 0.36mm
Therefore, the wire would stretch by 0.36 mm if it were twice as long.
Hence, option (A) is the correct answer.
To find: How much would the wire stretch if it were twice as long.
Solution:
Let us assume the original length of the wire as L and the elongation produced by the flood lamp as δL.
According to Hooke's law, stress is proportional to strain.
Hence, Stress/Strain = Constant (K)
Let us assume the constant K as k.
Therefore, Stress = k × Strain
The strain is given by the formula,
Strain (ε) = δL/L
Stress (σ) = F/A
where F is the force applied, and A is the cross-sectional area of the wire.
As the wire is hanging vertically, the force acting on the wire is its weight, which is given by:
F = mg
where m is the mass of the lamp, and g is the acceleration due to gravity.
Hence, the strain can be calculated as follows:
Strain (ε) = δL/L = σ/k
σ = F/A = mg/A
Thus, we have:
δL/L = σ/k = (mg/A)/k
δL = (mgL/kA)
As the stress is proportional to strain, we can write:
δL/L = K1
where K1 is the constant of proportionality.
Thus, we have:
K1 = δL/L = (mgL/kA)
Now, we need to find the elongation produced when the length of the wire is doubled.
Let the new length of the wire be 2L.
The new cross-sectional area of the wire is the same as the original one.
Hence, the new elongation produced can be calculated as follows:
δL' = K1 × 2L = 2K1L
δL' = 2(δL/L)L
δL' = 2(0.18mm/1m)1m
δL' = 0.36mm
Therefore, the wire would stretch by 0.36 mm if it were twice as long.
Hence, option (A) is the correct answer.
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Community Answer
You hang a flood lamp from the end of a vertical steel wire. The flood...
F/A=e/L
F/A=0.18/l ( let the length be l)
F/A=x/2l
0.18/L=x/2l
0.18×2l=xl
0.36l=xl
x=0.36
F/A=0.18/l ( let the length be l)
F/A=x/2l
0.18/L=x/2l
0.18×2l=xl
0.36l=xl
x=0.36
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You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer?
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You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer?.
You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer?.
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You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched if the wire were twice as long?a)0.36 mmb)0.34 mmc)0.38 mmd)0.40 mmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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