Question

In an experiment to measure the density of the material of a sphere, an error of \(2\%\) occurred while measuring the radius of a sphere and an error of \(3\%\) occurred while measuring the mass of the sphere. What is the maximum percentage error in the measurement of density?

• A. 8
• B. 6
• C. 7
• D. 9

Hint:

For powers, multiply percentage error by exponent. Here radius has power 3 → error becomes 3 times.

Answer 1

The Correct Option is D

Step 1: Formula for density.
\[ \rho = \frac{m}{V} \]

Step 2: Volume of sphere.
\[ V = \frac{4}{3}\pi r^3 \]
Thus,
\[ \rho \propto \frac{m}{r^3} \]

Step 3: Percentage error relation.
\[ \frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + 3\frac{\Delta r}{r} \]

Step 4: Substitute given errors.
\[ = 3\% + 3 \times 2\% \]

Step 5: Calculate.
\[ = 3\% + 6\% = 9\% \]

Step 6: Final conclusion.
\[ \boxed{9\%} \] Hence, correct answer is option (D).