Question

Length $l$ and Acceleration due to gravity $g$ are measured with $\pm 6\%$ and $\pm 4\%$ errors respectively. The percentage error in determination of the Time period of a simple pendulum will be,

• A. $\pm 7\%$
• B. $\pm 2\%$
• C. $\pm 5\%$
• D. $\pm 4\%$

Answer 1

The correct option is C $\pm 5\%$

From the formula
$T=2\pi \sqrt{\frac{l}{g}}$
Fractional error in the time period is
$\frac{\Delta T}{T}=[\frac{1}{2}\left(\frac{\Delta l}{l}\right)+\frac{1}{2}\left(\frac{\Delta g}{g}\right)]$
For percentage error
$\frac{\Delta T}{T}\times 100=[\frac{1}{2}\left(\frac{\Delta l}{l}\right)+\frac{1}{2}\left(\frac{\Delta g}{g}\right)]\times 100=\pm [(\frac{1}{2}\times 6)+(\frac{1}{2}\times 4)]=\pm 5\%$
So, $\%$ error in the time period is $\pm 5\%$
Hence, option (c) is the correct answer.