If T=2π((L/g))^(1/(2 )) and L=100±0.1 cm(limit standard error) T=2.01±0.01 s (limit standard error) Calculate the value of g and its standard error.


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Question Number 28929 by NECx last updated on 01/Feb/18

$I f T = 2 π {(\frac{L}{g})}^{\frac{1}{2}} a n d$ $L = 100 \pm 0.1 c m (l i m i t s t a n d a r d$ $e r r o r)$ $T = 2.01 \pm 0.01 s (l i m i t s t a n d a r d$ $e r r o r)$ $C a l c u l a t e t h e v a l u e o f g a n d i t s$ $s t a n d a r d e r r o r .$
	Answered by Tinkutara last updated on 02/Feb/18

	$g = \frac{4 π^{2} L}{T^{2}}$ $L = 1 \pm 10^{- 3} m$ $T = 2.01 \pm 0.01 s$ $g \approx 9.77 m / s^{2}$ $\frac{Δ g}{g} = \frac{Δ L}{L} + \frac{2 Δ T}{T}$ $Δ g = 9.77 (\frac{10^{- 3}}{1} + \frac{2 \times 0.01}{2.01}) \approx 0.107$ $\Rightarrow g = 9.77 \pm 0.107 m / s^{2}$
	Commented by NECx last updated on 03/Feb/18

	$w o w . . . T h a n k s$
	Commented by NECx last updated on 08/Feb/18

	$i t h i n k t h i s w a s f o r m a x i m u m$ $e r r o r .$
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