Question

The error in the measurement of length and mass is 3% and 4% respectively. The error in the measurement of density will be ______.

• A. 6%
• B. 13%
• C. 9%
• D. 15%

Hint:

In error analysis, NEVER subtract errors, even if variables are divided (like $M/L^3$)! We always want the MAXIMUM possible error, so we must add them up.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Density ($\rho$) is defined as $\text{Mass} / \text{Volume}$. For a linear object or a cube, Volume $\propto L^3$.

Step 2: Formula Application:
Relative error in density: $\frac{\Delta \rho}{\rho} = \frac{\Delta M}{M} + 3\frac{\Delta L}{L}$.

Step 3: Explanation:
Percentage error in Mass = 4%.
Percentage error in Length = 3%.
Total Error = $4% + 3(3%) = 4% + 9% = 13%$.

Step 4: Final Answer:
The error in density is 13%.