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The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%?
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?The density of a material in the shape of a cube is determined by mea...
Given:
- Relative error in measuring mass = 1.5%
- Relative error in measuring length = 1%
- The material is in the shape of a cube
To Find:
- Maximum error in determining the density
Formula:
Density (ρ) = Mass (m) / Volume (V)
Volume of a cube (V) = side^3
Explanation:
Let's assume the measured values for mass and length are m̂ and l̂ respectively. The actual values are m and l.
Relative error in measuring mass:
Error in mass (Δm) = m̂ - m
Relative error in mass = (Δm / m) * 100
Relative error in measuring length:
Error in length (Δl) = l̂ - l
Relative error in length = (Δl / l) * 100
Step 1: Calculate the relative error in measuring the volume of the cube.
Since the cube has equal sides, the relative error in measuring the length will be the same for all sides.
Relative error in measuring volume:
Error in volume (ΔV) = 3 * Δl
Relative error in volume = (ΔV / V) * 100
Step 2: Calculate the relative error in measuring the density.
Using the formula for density, we can express the relative error in density in terms of the relative errors in mass and volume.
Relative error in measuring density:
Error in density (Δρ) = Δm / m - ΔV / V
Relative error in density = (Δρ / ρ) * 100
Step 3: Substitute the given relative errors and calculate the maximum error in determining the density.
Relative error in measuring mass = 1.5%
Relative error in measuring volume = 3 * 1% = 3%
Relative error in density = (1.5% / 100) - (3% / 100)
Relative error in density = 0.015 - 0.03 = -0.015
The maximum error in determining the density is the absolute value of the relative error in density.
Maximum error in density = |-0.015| = 0.015 = 1.5%
Answer:
The maximum error in determining the density is 1.5%. Therefore, the correct option is (A) 2.5% (since it is the closest option to 1.5%).
- Relative error in measuring mass = 1.5%
- Relative error in measuring length = 1%
- The material is in the shape of a cube
To Find:
- Maximum error in determining the density
Formula:
Density (ρ) = Mass (m) / Volume (V)
Volume of a cube (V) = side^3
Explanation:
Let's assume the measured values for mass and length are m̂ and l̂ respectively. The actual values are m and l.
Relative error in measuring mass:
Error in mass (Δm) = m̂ - m
Relative error in mass = (Δm / m) * 100
Relative error in measuring length:
Error in length (Δl) = l̂ - l
Relative error in length = (Δl / l) * 100
Step 1: Calculate the relative error in measuring the volume of the cube.
Since the cube has equal sides, the relative error in measuring the length will be the same for all sides.
Relative error in measuring volume:
Error in volume (ΔV) = 3 * Δl
Relative error in volume = (ΔV / V) * 100
Step 2: Calculate the relative error in measuring the density.
Using the formula for density, we can express the relative error in density in terms of the relative errors in mass and volume.
Relative error in measuring density:
Error in density (Δρ) = Δm / m - ΔV / V
Relative error in density = (Δρ / ρ) * 100
Step 3: Substitute the given relative errors and calculate the maximum error in determining the density.
Relative error in measuring mass = 1.5%
Relative error in measuring volume = 3 * 1% = 3%
Relative error in density = (1.5% / 100) - (3% / 100)
Relative error in density = 0.015 - 0.03 = -0.015
The maximum error in determining the density is the absolute value of the relative error in density.
Maximum error in density = |-0.015| = 0.015 = 1.5%
Answer:
The maximum error in determining the density is 1.5%. Therefore, the correct option is (A) 2.5% (since it is the closest option to 1.5%).
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?The density of a material in the shape of a cube is determined by mea...
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?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%?
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?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%?.
?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about ?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ?The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (A) 2.5 % (B) 3.5 % (C) 4.5 % (D)6%?.
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