Question

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

• A. $\pm 8 \%$
• B. $\pm 5 \%$
• C. $\pm 3 \%$
• D. $\pm 6 \%$

Answer 1

Answer: (A)

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