First slide

Accuracy; precision of instruments and errors in measurements

Question

The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with Vernier Calipers having least count 0.01 cm. Given that length is 5.0 cm and radius is 2.00 cm. The percentage error in the calculated value of the volume will be

Moderate

A

1%
B

2%
C

3%
D

4%

Solution

Volume of cylinder $V = π r^{2} l$
Percentage error in volume
$\begin{matrix} \frac{Δ V}{V} \times 100 = \frac{2 Δ r}{r} \times 100 + \frac{Δ l}{l} \times 100 \\ = (2 \times \frac{0.01}{2.0} \times 100 + \frac{0.1}{5.0} \times 100) = (1 + 2) % = 3 % \end{matrix}$

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