The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r=(0.35± 0.05)… - JEE Main 2024 Physics PYQ

JEE Main 2024 — Physics Mechanics

2024mcqmedium

The radius $(r)$ , length $(l)$ and resistance $(R)$ of a metal wire was measured in the laboratory as

$r=(0.35\pm 0.05)\mathrm{cm}$ , $R=(100\pm 10)\mathrm{ohm}$ , $l=(15\pm 0.2)\mathrm{cm}$

The percentage error in resistivity of the material of the wire is :

Official previous-year question

Held on 1 Feb 2024 · Verified 6 Jul 2026.

Options

A
$25.6%$
B
$39.9%$
C
$37.3%$
D
$35.6%$

Did you get this right?

Solution

The resistance of the wire is given as, $R=\frac{\rho l}{A}$

Therefore, $\rho =R\frac{A}{l}$

$\rho =R\frac{(\pi {r}^{2})}{l}$

For percentage error, we can write $\frac{\Delta \rho }{\rho }=\frac{\Delta R}{R}+2\frac{\Delta r}{r}+\frac{\Delta l}{l}$

$\frac{\Delta \rho }{\rho }\times 100=\frac{\Delta R}{R}\times 100+2\frac{\Delta r}{r}\times 100+\frac{\Delta l}{l}\times 100$

$=(\frac{10}{100}+2\times \frac{0.05}{0.35}+\frac{0.2}{15})\times 100$

$=(\frac{1}{10}+\frac{2}{7}+\frac{1}{75})\times 100$

Hence, $\frac{\Delta \rho }{\rho }=39.9%$

Your note

JEE Main Mechanics in other years

Mechanics 2026 Mechanics 2025 Mechanics 2023 Mechanics 2022 Mechanics 2021 Mechanics 2020 Mechanics 2019 Mechanics 2018 Mechanics 2017 Mechanics 2016 Mechanics 2015 Mechanics 2014

Keep practicing Mechanics

Work through every JEE Main Mechanics PYQ, year by year.

Browse all Physics topics

Solution

The resistance of the wire is given as, $R=\frac{\rho l}{A}$

Therefore, $\rho =R\frac{A}{l}$

$\rho =R\frac{(\pi {r}^{2})}{l}$

For percentage error, we can write $\frac{\Delta \rho }{\rho }=\frac{\Delta R}{R}+2\frac{\Delta r}{r}+\frac{\Delta l}{l}$

$\frac{\Delta \rho }{\rho }\times 100=\frac{\Delta R}{R}\times 100+2\frac{\Delta r}{r}\times 100+\frac{\Delta l}{l}\times 100$

$=(\frac{10}{100}+2\times \frac{0.05}{0.35}+\frac{0.2}{15})\times 100$

$=(\frac{1}{10}+\frac{2}{7}+\frac{1}{75})\times 100$

Hence, $\frac{\Delta \rho }{\rho }=39.9%$

Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics

Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics