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The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60±0.003) g, radius of wire =(0.50±0.01) cm, length of wire =(10.00±0.05) cm]

Asked in JEE Main 22nd Jan 2nd Shift 2025 · Percentage error in a derived quantity

Answer: (1) 5

Step-by-step solution

Given: m=0.60±0.003 g, r=0.50±0.01 cm, l=10.00±0.05 cm.

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

(Δρ)/ρ=(Δ m)/m+2(Δ r)/r+(Δ l)/l

=(0.003)/(0.60)+2×(0.01)/(0.50)+(0.05)/(10.00)

=0.005+0.040+0.005=0.05, that is 5%.

Why the other options are wrong

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