To find the spring constant (k) of a spring experimentally, a stu… - Vidyadip

MCQ

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 :

A
$3 \%$
B
$1 \%$
C
$4 \%$
✓
$5 \%$

✓

Answer

Correct option: D.

$5 \%$

d
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$

$\mathrm{T}^2 \propto \frac{\mathrm{m}}{\mathrm{k}}$

$\frac{2 \Delta \mathrm{T}}{\mathrm{T}} \%=\frac{\Delta \mathrm{m}}{\mathrm{m}} \%-\frac{\Delta \mathrm{k}}{\mathrm{k}} \%$

$\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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