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A silver wire has a mass (0.6±0.006) g, radius (0.5±0.005) mm and length (4±0.04) cm. The maximum percentage error in the measurement of its density will be

Asked in JEE Main 27th June 1st Shift 2022 · Percentage error in a derived quantity

Answer: (1) 4%

Step-by-step solution

Given: m=0.6±0.006 g, r=0.5±0.005 mm, l=4±0.04 cm.

Idea: ρ=m/(π r²l), so the radius enters squared.

(Δρ)/ρ=(Δ m)/m+2(Δ r)/r+(Δ l)/l

=(0.006)/(0.6)+2×(0.005)/(0.5)+(0.04)/4

=0.01+0.02+0.01=0.04, that is 4%.

Why the other options are wrong

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