To find the spring constant $(k)$ of a spring experimentally, a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in measurement of mass. The percentage error in determining value of $\mathrm{k}$ is :
JEE MAIN 2024, Diffcult
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$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
$\mathrm{T}^2 \propto \frac{\mathrm{m}}{\mathrm{k}}$
$\frac{2 \Delta \mathrm{T}}{\mathrm{T}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{\Delta \mathrm{k}}{\mathrm{k}} \%$
$\frac{\Delta \mathrm{k}}{\mathrm{k}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{2 \Delta \mathrm{T}}{\mathrm{T}} \% $
$\frac{\Delta \mathrm{k}}{\mathrm{k}} \%=(-1) \%-2(2) \%=|-5 \%|=5 \%$
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