First slide

Accuracy; precision of instruments and errors in measurements

Question

The mass of a body is 20.000 g and its volume is 10.00 cm³. If the measured values are expressed to the correct significant figures, the maximum error in the value of density is

Moderate

A

$0.001 g {cm}^{- 3}$
B

$0.010 g {cm}^{- 3}$
C

$0.100 g {cm}^{- 3}$
D

none of these

Solution

Maximum error in measuring mass = 0.001 g, because least count is 0.001 g, Similarly, maximum error in measuring volume is 0.01 cm³.
$\begin{array}{l} \frac{Δ ρ}{ρ} = \frac{Δ M}{M} + \frac{Δ V}{V} = \frac{0.001}{20.000} + \frac{0.01}{10.00} \\ = (5 \times 10^{- 5}) + (1 \times 10^{- 3}) = 1.05 \times 10^{- 3} \\ Δ ρ = (1.05 \times 10^{- 3}) \times ρ \\ = 1.05 \times 10^{- 3} \times \frac{20.000}{10.00} = 0.002 g {cm}^{- 3} \end{array}$

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