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EEJ MAIN Physics QUESTION #7036
Question 1
The density of a cube is calculated by measuring its mass and the length of its sides. If the relative error in mass is $1.5\%$ and in length is $1\%$, determine the maximum percentage error in the density.
  • $4.5\%$✔️
  • $6\%$
  • $2.5\%$
  • $3.5\%$
Correct Answer Explanation

Density ($\rho$) is given by: $\rho = \frac{M}{L^3}$

The relative error formula for density is:

$\frac{\Delta \rho}{\rho} \times 100 = \frac{\Delta M}{M} \times 100 + 3 \left( \frac{\Delta L}{L} \times 100 \right)$

Substitute the given values:

$\text{Max Error} = 1.5\% + 3(1\%) = 4.5\%$