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

Correct answer: (C) 4%. Volume of the wire is V=πr^2l. Density of the wire is ρ=m/(πr^2l) Relative error in measurement of density ⇒(Δρ)/(ρ)=(Δm)/m+2×(Δr)/r+(Δl)/l =0.006/0.6+2×0.005/0.5+0.04/4 =0.01+0.02+0.01=0.04 ∴ Percentage error in ρ=0.04×100=4%

Q63 / 90 · JEE Main 2022 (27 Jun Shift 1) · Physics

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

A
$7 %$
B
$3 %$
Correct answer
C
$4 %$
D
$6 %$

Solution

Volume of the wire is $V = π r^{2} l$ .

Density of the wire is $ρ = \frac{m}{π r^{2} l}$

Relative error in measurement of density

$\Rightarrow \frac{Δ ρ}{ρ} = \frac{Δ m}{m} + 2 \times \frac{Δ r}{r} + \frac{Δ l}{l}$

$= \frac{0.006}{0.6} + 2 \times \frac{0.005}{0.5} + \frac{0.04}{4}$

$= 0.01 + 0.02 + 0.01 = 0.04$

$∴$ Percentage error in $ρ = 0.04 \times 100 = 4 %$

Hence, the correct answer is option: 'C'.

Relevant Questions

The density of a uniform cylinder is determined by measuring its mass , length and diameter . The measured values of , and are g, mm and mm,06 Apr, 2026 (M)Errors of Measurement
Four persons measure the length of a rod as and 18.25 cm. The relative error in the measurement of average length of the rod is :23 Jan, 2026 (M)Errors of Measurement
In an experiment the values of two spring constants were measured as and . If these springs are connected in parallel, then the percentage e21 Jan, 2026 (M)Errors of Measurement
A quantity Q is formulated as and Z are independent parameters which have fractional errors of and 0.5 , respectively in measurement. The ma08 Apr, 2025 (E)Errors of Measurement
A physical quantity C is related to four other quantities and s as follows The percentage errors in the measurement of and s are and respect03 Apr, 2025 (E)Errors of Measurement
A physical quantity is related to four observables as follows : where, and , then the percentage error in Q is , where ________ .29 Jan, 2025 (E)Errors of Measurement