Question

The error in the measurement of the length of a simple pendulum is 0.1% and the error in the time period is 3%. The maximum possible error in the measurement of $g$ is _____.

$T=2\pi \sqrt{\frac{l}{g}}$

• A. 6.1%
• B. 6.0%
• C. 3.1%
• D. 6.2%

Answer 1

The correct option is A 6.1%

$T=2\pi \sqrt{\frac{l}{g}}$

$\sqrt{g}=2\pi \frac{\sqrt{l}}{T}$

$\frac{1}{2}\frac{\Delta g}{g}=\frac{\Delta T}{T}+\frac{1}{2}\frac{\Delta l}{l}$

$\frac{1}{2}\frac{△g}{g}=\mid 3\mid +\frac{1}{2}\times |0.1|$

$\Rightarrow \frac{△g}{g}=6.1\%$

The maximum possible error, $\frac{△g}{g}=6.1\%$