First slide

Errors

Question

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

Moderate

A

12%
B

14%
C

7%
D

9%

Solution

Maximum error in mass $(\frac{Δ m}{m}) = 3 % = \frac{3}{100}$ and maximum error in length $(\frac{Δ l}{l}) = 2 % = \frac{2}{100}$ Maximum error in the measurement of density
$\begin{aligned} \frac{Δ ρ}{ρ} = \frac{Δ m}{m} + (3 \times \frac{Δ l}{l}) = \frac{3}{100} + (3 \times \frac{2}{100}) = \frac{3}{100} + \frac{6}{100} \\ = \frac{9}{100} = 9 % \end{aligned}$

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