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JEE Main 202522 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Evening Shift
Subject
Physics
Chapter
Mathematics in Physics

JEE Main 2025 · 22 January · Evening Shift · Physics · Mathematics in Physics

The maximum percentage error in the measurment of density of a wire...

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

Options

  1. A8
  2. B5
  3. C4
  4. D7

Correct answer

B. 5

Step-by-step solution

d=m vol. =mπR2ℓ⇒dρρ=dmm+2dRR+dℓℓ⇒dρρ=(0.0030.6+2×0.010.5+0.0510)100=5%\begin{aligned} & \mathrm{d}=\frac{\mathrm{m}}{\text{ vol. }}=\frac{\mathrm{m}}{\pi \mathrm{R}^2 \ell} \Rightarrow \frac{\mathrm{ d} \rho}{\rho}=\frac{\mathrm{dm}}{\mathrm{m}}+\frac{2 \mathrm{dR}}{\mathrm{R}}+\frac{\mathrm{d} \ell}{\ell} \\ & \Rightarrow \frac{\mathrm{d} \rho}{\rho}=\left(\frac{0.003}{0.6}+\frac{2 \times 0.01}{0.5}+\frac{0.05}{10}\right) 100=5 \%\end{aligned}
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