Question

If mass, radius of cross-section and height of a cylinder are (0.4+0.01) g, (6+0.03) m and height (8+0.04) m. The maximum percentage error in the measurement of density of cylinder is?

• A. 1%
• B. 4%
• C. 8%
• D. 7%

Answer 1

The Correct Option is B

Step 1: Use the formula for density and apply error propagation principles.- Given m = (0.4±0.01)g, ℓ = (8±0.04)cm, r = (6±0.03)mm.- Density ρ = $\frac{m}{\pi r^2 \ell}$.- Differentiate logarithmically:- Substitute:

$\frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + \frac{\Delta \ell}{\ell} + 2\frac{\Delta r}{r}$ .

$\frac{\Delta \rho}{\rho} = \frac{0.01}{0.4} + \frac{0.04}{8} + 2\frac{0.03}{6}$ .

Step 2: Simplify the calculations.

$\frac{\Delta \rho}{\rho} = 0.025 + 0.005 + 0.01 = 0.04$.

Final Answer: Maximum error in density = 0.04 × 100 = 4%.