Mass = \( (28 \pm 0.01) \, \text{g} \), Volume = \( (5 \pm 0.1) \, \text{cm}^3 \). What is the percentage error in density?
The density \( \rho \) of an object is calculated using the formula: \[ \rho = \frac{\text{Mass}}{\text{Volume}} \]. The provided values are: Mass = \( 28 \pm 0.01 \) g and Volume = \( 5 \pm 0.1 \) cm³. The formula for the percentage error in density is: \[ \% \, \text{error in density} = \left( \frac{\Delta m}{m} + \frac{\Delta V}{V} \right) \times 100 \]. Here, \( \Delta m = 0.01 \, \text{g} \) represents the uncertainty in mass, \( m = 28 \, \text{g} \) is the mass, \( \Delta V = 0.1 \, \text{cm}^3 \) is the uncertainty in volume, and \( V = 5 \, \text{cm}^3 \) is the volume. Substituting these values into the error formula yields: \[ \% \, \text{error in density} = \left( \frac{0.01}{28} + \frac{0.1}{5} \right) \times 100 \]. Calculating the individual percentage errors: \( \frac{0.01}{28} \approx 0.000357 \) and \( \frac{0.1}{5} = 0.02 \). Summing these errors gives: \[ \% \, \text{error in density} = (0.000357 + 0.02) \times 100 = 2.0357 \% \]. Therefore, the percentage error in density is approximately \( 3.57 \% \).