A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be:
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Question

A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be:

G1 Physics · Accepted Answer

Step 1: For a cylindrical wire, ρ=m/(πr²L). Step 2: Maximum fractional error is Δm/m + 2Δr/r + ΔL/L. Step 3: Percentage = (0.002/0.4 + 2×0.001/0.3 + 0.02/5)×100 ≈ 1.57% ≈1.6%. Final: Option A.