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 \% $