Error Analysis: Practice Problem & Solution
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]
Solution Explained:
To solve this problem, we apply the core principles of Error Analysis. Understanding the underlying formula is key to arriving at the correct answer below:
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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