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A volume is measured as 2.0 L with an uncertainty of ±0.1 L. If this volume is u

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Question: A volume is measured as 2.0 L with an uncertainty of ±0.1 L. If this volume is used to calculate density, what is the uncertainty in density if mass is measured as 4.0 kg with an uncertainty of ±0.2 kg?

Options:

  1. 0.1 kg/L
  2. 0.2 kg/L
  3. 0.05 kg/L
  4. 0.4 kg/L

Correct Answer: 0.1 kg/L

Solution: 

Using the formula for density (density = mass/volume), the uncertainty in density can be calculated using the formula for propagation of uncertainty.

A volume is measured as 2.0 L with an uncertainty of ±0.1 L. If this volume is u

Practice Questions

Q1
A volume is measured as 2.0 L with an uncertainty of ±0.1 L. If this volume is used to calculate density, what is the uncertainty in density if mass is measured as 4.0 kg with an uncertainty of ±0.2 kg?
  1. 0.1 kg/L
  2. 0.2 kg/L
  3. 0.05 kg/L
  4. 0.4 kg/L

Questions & Step-by-Step Solutions

A volume is measured as 2.0 L with an uncertainty of ±0.1 L. If this volume is used to calculate density, what is the uncertainty in density if mass is measured as 4.0 kg with an uncertainty of ±0.2 kg?
Correct Answer: ±0.1 kg/L
  • Step 1: Identify the formula for density, which is density = mass / volume.
  • Step 2: Write down the values given: mass = 4.0 kg with an uncertainty of ±0.2 kg, and volume = 2.0 L with an uncertainty of ±0.1 L.
  • Step 3: Calculate the density using the values: density = 4.0 kg / 2.0 L = 2.0 kg/L.
  • Step 4: Use the formula for propagation of uncertainty for division: if z = x / y, then the relative uncertainty in z is given by (Δz/z) = (Δx/x) + (Δy/y).
  • Step 5: Calculate the relative uncertainty in mass: Δm/m = 0.2 kg / 4.0 kg = 0.05.
  • Step 6: Calculate the relative uncertainty in volume: ΔV/V = 0.1 L / 2.0 L = 0.05.
  • Step 7: Add the relative uncertainties: 0.05 + 0.05 = 0.10.
  • Step 8: Calculate the absolute uncertainty in density: Δdensity = density * (relative uncertainty) = 2.0 kg/L * 0.10 = 0.2 kg/L.
  • Step 9: Write the final result: The density is 2.0 kg/L with an uncertainty of ±0.2 kg/L.
  • Propagation of Uncertainty – This concept involves calculating the uncertainty in a derived quantity (density) based on the uncertainties in the measured quantities (mass and volume).
  • Density Calculation – Understanding the formula for density (density = mass/volume) and how to apply it in the context of measurements with uncertainties.
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