Question

The mass of an object is measured as \( (28 \pm 0.01) \) g and its volume as \( (5 \pm 0.1) \) cm\(^3\). What is the percentage error in density?

• A. 1.20\%
• B. 2.04\%
• C. 0.35\%
• D. 0.71\%

Hint:

When calculating the percentage error in density, use the formula for error propagation for division, which adds the relative errors in mass and volume.

Answer 1

The Correct Option is C

The density \( \rho \) is given by: \[ \rho = \frac{m}{V} \] Where: - \( m = 28 \) g and the uncertainty in mass \( \Delta m = 0.01 \) g, - \( V = 5 \) cm\(^3\) and the uncertainty in volume \( \Delta V = 0.1 \) cm\(^3\). The percentage error in density is calculated using the formula for error propagation for division: \[ \frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + \frac{\Delta V}{V} \] Substituting the values: \[ \frac{\Delta \rho}{\rho} = \frac{0.01}{28} + \frac{0.1}{5} \] \[ \frac{\Delta \rho}{\rho} = 0.000357 + 0.02 = 0.020357 \approx 0.35\% \] Thus, the percentage error in density is \( 0.35\% \).