Source: Extra Practice

The mass and volume of a body are found to be 5.00±0.05 kg5.00 \pm 0.05\text{ kg} and 1.00±0.05 m31.00 \pm 0.05\text{ m}^3 respectively. Then the maximum possible percentage error in its density is:

Options

Option A is correct

6%

Option B

1%

Option C

10%

Option D

5%

Explanation

Density ρ=mass/volume\rho = \text{mass}/\text{volume}. The relative error in density is Δρρ=Δmm+ΔVV\frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + \frac{\Delta V}{V}. Plugging in the values: Δρρ=0.055.00+0.051.00=0.01+0.05=0.06\frac{\Delta \rho}{\rho} = \frac{0.05}{5.00} + \frac{0.05}{1.00} = 0.01 + 0.05 = 0.06. Multiplying by 100100 to get the percentage error gives 6%6\%. This represents the maximum possible uncertainty in the density value.