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  4. What is the fractional error in g calculated from T=2 π √g ? Given fraction errors in T and are ± x and ± y respectively.

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Q. What is the fractional error in $g$ calculated from $T=2 \pi \sqrt{g } ?$ Given fraction errors in $T$ and are $\pm x$ and $\pm y$ respectively.

JIPMERJIPMER 2018

Solution:

From $T=2 \sqrt{\frac{ }{g}}; g=4 ^{2} \frac{ }{T^{2}}$
$\frac{g}{g}=\frac{ }{ }+\frac{2\quad T}{T}=\left(y +2x\right)$