If-T-2pi-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-

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 \dots 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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