Mathematics in Physics

JEE Main level, single correct, medium

64 of 121

Question 64 of 121

To find the spring constant (k)(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 kk is :

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Answer: (A) 5%5 \%

T=2πmkT2∝mk2ΔTT%=Δmm%−Δkk%Δkk%=Δmm%−2ΔTT%Δkk%=(−1)%−2(2)%=∣−5%∣=5%\begin{aligned} & \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 \%\end{aligned}

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