Question

The errors in the measurement of mass and length of the cube is $1.5%$ and $2.5%$ respectively. The percentage error in the measurement of density of a cube is

• A. $3%$
• B. $1.5%$
• C. $6%$
• D. $9%$

Hint:

Powers in formula multiply the percentage error directly.

Answer 1

The Correct Option is D

Step 1: Formula for density.
\[ \rho = \frac{m}{l^3} \]
Step 2: Error propagation rule.
For a quantity $Q = \dfrac{A}{B^n}$, percentage error is:
\[ %\Delta Q = %\Delta A + n\,%\Delta B \]
Step 3: Applying given errors.
\[ %\Delta \rho = 1.5% + 3 \times 2.5% \] \[ %\Delta \rho = 1.5% + 7.5% = 9% \]
Step 4: Conclusion.
The percentage error in density is $9%$.