The error in the measurement of length of a simple pendulum is $0.1\%$ and error in the time period is $2 \%$. The possible maximum error in the quantity having dimensional formula $LT^{-2}$ is

Given,

Error $\%$ in time $=2\%=\dfrac{2}{100}=\dfrac{1}{50}=2\%$

Error $\%$ in length $=0.1\%$

Find $\%$ error in $\dfrac{1}{12}$

$\therefore$ as $\dfrac{\triangle A}{A}=\left( \dfrac{\triangle 2}{2}\right) +\left( \dfrac{\triangle Q}{Q}\right)$ if $A=\dfrac{t}{Q}$

Thus,

$\Rightarrow \%$ error $=\left( \dfrac{\triangle L}{L}\right) +2\left( \dfrac{\triangle T}{T}\right)$

$=\left( 2\%\right) +2\left( .1\%\right)$

$=2\%+.2\%$

$=2.2\%$

Hence, the answer is $2.2\%.$