Question

In a simple pendulum experiment, the maximum percentage error in the measurement of length is $2\%$ and that in the observation of the time-period is $3\%$ . Then the maximum percentage error in determination of the acceleration due to gravity $g$ is

• A. 5%
• B. 6%
• C. 7%
• D. 8%
• E. 10%

Answer 1

Answer: (D)

The maximum percentage error
$\frac{\Delta g}{g}=\frac{\Delta l}{l}+{\left|\frac{\Delta T}{T}\right|}^2$
$=\frac{\Delta l}{l}+2\frac{\Delta T}{T}$ where $\frac{\Delta l}{l}=2\%$
$\frac{\Delta g}{g}=2\%+2\times 3\%\frac{\Delta T}{T}=3\%$
$=2\%+6\%=8\%$