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What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.
- a)0.04
- b)0.4
- c)4
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
What will be the maximum percentage error in the measurement of the de...
Calculation of Maximum Percentage Error:
- Given measurements:
- Radius = (4 ± 0.004) cm
- Length = (8 ± 0.008) cm
- Mass = (30 ± 0.03) g
Density Calculation:
- Density (ρ) = Mass / (π * Radius^2 * Length)
- Substituting the values:
- Density (ρ) = 30 / (π * 4^2 * 8) = 30 / (π * 16 * 8) = 30 / (128π) ≈ 0.0737 g/cm^3
Maximum Percentage Error Formula:
- Maximum error in density = |∂ρ/ρ| * 100%
- Where |∂ρ| = |(∂ρ/∂m) * Δm + (∂ρ/∂r) * Δr + (∂ρ/∂l) * Δl|
- Calculating the partial derivatives and plugging in the values:
- |∂ρ| = |(1/(π * r^2 * l)) * Δm + (-2m/(π * r^3 * l)) * Δr + (-m/(π * r^2 * l^2)) * Δl|
- |∂ρ| = |(1/(π * 4^2 * 8)) * 0.03 + (-2*30/(π * 4^3 * 8)) * 0.004 + (-30/(π * 4^2 * 8^2)) * 0.008|
- |∂ρ| ≈ |0.0001 + 0.0007 - 0.0024| = 0.0004
Maximum Percentage Error Calculation:
- Maximum error in density = |0.0004 / 0.0737| * 100% ≈ 0.542%
Therefore, the maximum percentage error in the measurement of the density of the iron rod is approximately 0.54%, which is closest to option B (0.4).
- Given measurements:
- Radius = (4 ± 0.004) cm
- Length = (8 ± 0.008) cm
- Mass = (30 ± 0.03) g
Density Calculation:
- Density (ρ) = Mass / (π * Radius^2 * Length)
- Substituting the values:
- Density (ρ) = 30 / (π * 4^2 * 8) = 30 / (π * 16 * 8) = 30 / (128π) ≈ 0.0737 g/cm^3
Maximum Percentage Error Formula:
- Maximum error in density = |∂ρ/ρ| * 100%
- Where |∂ρ| = |(∂ρ/∂m) * Δm + (∂ρ/∂r) * Δr + (∂ρ/∂l) * Δl|
- Calculating the partial derivatives and plugging in the values:
- |∂ρ| = |(1/(π * r^2 * l)) * Δm + (-2m/(π * r^3 * l)) * Δr + (-m/(π * r^2 * l^2)) * Δl|
- |∂ρ| = |(1/(π * 4^2 * 8)) * 0.03 + (-2*30/(π * 4^3 * 8)) * 0.004 + (-30/(π * 4^2 * 8^2)) * 0.008|
- |∂ρ| ≈ |0.0001 + 0.0007 - 0.0024| = 0.0004
Maximum Percentage Error Calculation:
- Maximum error in density = |0.0004 / 0.0737| * 100% ≈ 0.542%
Therefore, the maximum percentage error in the measurement of the density of the iron rod is approximately 0.54%, which is closest to option B (0.4).
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Community Answer
What will be the maximum percentage error in the measurement of the de...
Density of the rod will be calculated as
The percentage error will be calculated as
Substituting the values in the above equation
= (0.001 + 0.002 + 0.001) × 100 = 0.4%
Therefore, it is our required solution.
The percentage error will be calculated as
Substituting the values in the above equation
= (0.001 + 0.002 + 0.001) × 100 = 0.4%
Therefore, it is our required solution.
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What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer?
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What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer?.
What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the maximum percentage error in the measurement of the density of an iron rod whose radius and length are measured as (4 ± 0.004) cm and (8 ± 0.008) cm respectively? The mass of the wire is measured to be (30 ± 0.03) g.a)0.04b)0.4c)4d)40Correct answer is option 'B'. Can you explain this answer?.
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