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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?
Most Upvoted Answer
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.
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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?.
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