First slide

Accuracy; precision of instruments and errors in measurements

Question

The density of a cube is measured by measuring its mass and length of its sides. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the measurement of density is

Moderate

A

7%
B

5%
C

1%
D

9%

Solution

We know density
, $\begin{array}{l} ρ = \frac{M}{V} = \frac{[M]}{[L^{3}]} \\ ∴ \frac{Δρ}{ρ} \times 100 = \frac{ΔM}{M} \times 100 + 3 \frac{ΔL}{L} \times 100 \\ = 3 % + 3 (2 %) = 9 % \end{array}$

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