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A certain body weighs 22.42 gm and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 gm and 0.1 cc. Then maximum error in the density will be:

1. 22%
2. 2%
3. 0.2%
4. 0.02%

Correct answer: 2%

Solution

The formula for density is ρ = m/V. The relative error in density is given by the sum of the relative errors in mass and volume: Δρ/ρ = Δm/m + ΔV/V. Substituting the given values, Δm/m = 0.01/22.42 and ΔV/V = 0.1/4.7. Adding these gives approximately 0.02 or 2% as the maximum error.

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