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Physics · Units, Dimensions & Error Analysis

JEE Main 2024 — 6 April, Shift 1 — Question 31

To find the spring constant (k)(\mathrm{k}) of a spring experimentally, a student commits 2%2 \% positive error in the measurement of time and 1%1 \% negative error in measurement of mass. The percentage error in determining value of k is :

  1. Option A:

    3%3 \%

  2. Option B:

    1%1 \%

  3. Option C:

    4%4 \%

  4. Option D:

    5%5 \%

    Correct

Answer: D

Step-by-step solution

T=2π mkT=2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}}

T2∝ mk\mathrm{T}^{2} \propto \frac{\mathrm{~m}}{\mathrm{k}}

2Δ T T%=Δmm%−Δkk%\frac{2 \Delta \mathrm{~T}}{\mathrm{~T}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{\Delta \mathrm{k}}{\mathrm{k}} \%

Δkk%=Δmm%−2Δ T T%\frac{\Delta \mathrm{k}}{\mathrm{k}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{2 \Delta \mathrm{~T}}{\mathrm{~T}} \% Δkk%=(−1)%−2(2)%=∣−5%∣=5%\frac{\Delta \mathrm{k}}{\mathrm{k}} \%=(-1) \%-2(2) \%=|-5 \%|=5 \%

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
6 April, Shift 1
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Significant Figures and Error Analysis

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