A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate $g$, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage…

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A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate $g$, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is

Aicharya · Accepted Answer

$\begin{aligned} & h=\frac{1}{2} g t^2 \ & 	ext { or } \quad g=\frac{\mathrm{2h}}{\mathrm{t}^2} \ & 	herefore \quad \log \mathrm{g}=\log \mathrm{h}-2 \log \mathrm{t} \ & \left(\frac{\Delta g}{g} 	imes 100ight)_{\max }=\left(\frac{\Delta \mathrm{h}}{\mathrm{h}} 	imes 100ight)+2\left(\frac{\Delta \mathrm{t}}{\mathrm{t}} 	imes 100ight) \ & =\mathrm{e}_1+2 \mathrm{e}_2 \ & \end{aligned}$

A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses…

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