Percentage Error in Density of a Cube – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Error Analysis

Percentage Error in Density of a Cube

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:

[1996]

12%
14%
7%
9%

Solution:

Density of a cube \(\rho = M/L^3\). Percentage error in \( \rho = (\Delta M/M) + 3(\Delta L/L)\). Given \(\Delta M/M \times 100% = 3%\) and \(\Delta L/L \times 100% = 2%\). So, Percentage error in \(\rho \) = 3% + 3(2%) = 3% + 6% = 9% .

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