A wire has corrected diameter 0.50 mm. If the instrumental uncertainty in diameter is one least count = 0.01 mm, enter the approximate percentage uncertainty in its calculated cross-sectional area.
Physics · Unit dimension and error · vernier callipers and screw gauge
JEE Mains NEET

Question

A wire has corrected diameter 0.50 mm. If the instrumental uncertainty in diameter is one least count = 0.01 mm, enter the approximate percentage uncertainty in its calculated cross-sectional area.

G1 Physics · Accepted Answer

For A ∝ d², percentage uncertainty in area ≈ 2(Δd/d) × 100 = 2(0.01/0.50) × 100 = 4%.