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)

$8\%$

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

or $g=\frac{4{\pi }^{2}l}{T^2}$

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