To estimate ' g ' from g=4 π2 (L/T2), error in measurement of L is ± 2 % and error in measurement T is ± 3 %. The error in estimated ' g ' will be

Question

To estimate ' g ' from g=4 π2 (L/T2), error in measurement of L is ± 2 % and error in measurement T is ± 3 %. The error in estimated ' g ' will be (A) ± 8 % (B) ± 5 % (C) ± 3 % (D) ± 6 %

Tardigrade Admin · Accepted Answer

∵ g=4 π2 (L/T2) Percentage error in the estimation of g is given as, (Δ g/g) × 100=±((Δ L/L) × 100+2 (Δ T/T) × 100) =±(2 %+2 × 3 %) =±(2 %+6 %)=± 8 %

Q. To estimate ' $g$ ' from $g = 4 π^{2} \frac{L}{T ^{2}}$ , error in measurement of $L$ is $\pm 2%$ and error in measurement $T$ is $\pm 3%$ . The error in estimated ' $g$ ' will be

$\pm 8%$

$\pm 5%$

$\pm 3%$

$\pm 6%$

$∵ g = 4 π^{2} \frac{L}{T ^{2}}$
Percentage error in the estimation of $g$ is given as,
$\frac{Δ g}{g} \times 100 = \pm (\frac{Δ L}{L} \times 100 + 2 \frac{Δ T}{T} \times 100)$
$= \pm (2% + 2 \times 3%)$
$= \pm (2% + 6%) = \pm 8%$

Q. To estimate ' g ' from g=4π2T2L​, error in measurement of L is ±2% and error in measurement T is ±3%. The error in estimated ' g ' will be

±8%

±5%

±3%

±6%