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A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4?
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A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06...
Solution:
Given: mass (m) = 0.3 ± 0.003 g, radius (r) = 0.5 ± 0.005 mm and length (l) = 6 ± 0.06 cm.
The maximum percentage error in the measurement of density can be calculated by using the formula:
Density (ρ) = mass/volume
Volume (V) = πr²l
Calculation of the volume:
The volume of the wire can be calculated as follows:
V = πr²l
V = π(0.5 ± 0.005 mm)²(6 ± 0.06 cm)
V = π(0.5 ± 0.005 mm)²(0.06 ± 0.0006 m)
V = π(0.00025 ± 0.000005) m²(0.06 ± 0.0006) m
V = (4.71 ± 0.09) x 10^-6 m^3
Calculation of the density:
The density of the wire can be calculated as follows:
ρ = m/V
ρ = (0.3 ± 0.003) g/(4.71 ± 0.09) x 10^-6 m^3
ρ = (0.3 ± 0.003) g/(4.71 ± 0.09) cm^3
ρ = (0.3 ± 0.003)/(4.71 ± 0.09) g/cm^3
ρ = 0.0635 ± 0.0014 g/cm^3
Calculation of the maximum percentage error:
The maximum percentage error can be calculated as follows:
Maximum percentage error = (Absolute error/True value) x 100
Absolute error = ± 0.0014 g/cm^3
True value = 0.0635 g/cm^3
Maximum percentage error = (± 0.0014/0.0635) x 100
Maximum percentage error = ± 2.2%
Conclusion:
Therefore, the maximum percentage error in the measurement of the density of the wire is 2.2%, which is approximately equal to 2%. Therefore, the correct option is (b) 2.
Given: mass (m) = 0.3 ± 0.003 g, radius (r) = 0.5 ± 0.005 mm and length (l) = 6 ± 0.06 cm.
The maximum percentage error in the measurement of density can be calculated by using the formula:
Density (ρ) = mass/volume
Volume (V) = πr²l
Calculation of the volume:
The volume of the wire can be calculated as follows:
V = πr²l
V = π(0.5 ± 0.005 mm)²(6 ± 0.06 cm)
V = π(0.5 ± 0.005 mm)²(0.06 ± 0.0006 m)
V = π(0.00025 ± 0.000005) m²(0.06 ± 0.0006) m
V = (4.71 ± 0.09) x 10^-6 m^3
Calculation of the density:
The density of the wire can be calculated as follows:
ρ = m/V
ρ = (0.3 ± 0.003) g/(4.71 ± 0.09) x 10^-6 m^3
ρ = (0.3 ± 0.003) g/(4.71 ± 0.09) cm^3
ρ = (0.3 ± 0.003)/(4.71 ± 0.09) g/cm^3
ρ = 0.0635 ± 0.0014 g/cm^3
Calculation of the maximum percentage error:
The maximum percentage error can be calculated as follows:
Maximum percentage error = (Absolute error/True value) x 100
Absolute error = ± 0.0014 g/cm^3
True value = 0.0635 g/cm^3
Maximum percentage error = (± 0.0014/0.0635) x 100
Maximum percentage error = ± 2.2%
Conclusion:
Therefore, the maximum percentage error in the measurement of the density of the wire is 2.2%, which is approximately equal to 2%. Therefore, the correct option is (b) 2.
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A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4?
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A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4?.
A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire has a mass 0.3 ± 0.003g, radius 0.5± 0.005 mm and length 6±0.06 cm. The maximum percentage error in the measurement of its density is(a) 1 (b) 2 (c) 3 (d) 4?.
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