If the errors in the measurement of $l$ and $g$ are $2 \%$ and $4 \%$ respectively, the percentage o

Question

If the errors in the measurement of $l$ and $g$ are $2 \%$ and $4 \%$ respectively, the percentage of error in the time period of pendulum is

Professor PC Thomas Classes · Answer

$T = 2\pi\sqrt{l/g} \Rightarrow \frac{\Delta T}{T} = \frac{1}{2}\frac{\Delta l}{l} + \frac{1}{2}\frac{\Delta g}{g} = \frac{1}{2}(2) + \frac{1}{2}(4) = 3\%$.