$A$ force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$,what is the maximum percentage error in pressure (in $\%$)?

The mass of an object is measured as $225 \pm 0.05 \, g$. Find the percentage error in this measurement. (in $\%$)

In an experiment to determine the acceleration due to gravity $g$,the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \text{ mm}$ and $(10 \pm 1) \text{ mm}$,respectively. In five successive measurements,the time period is found to be $0.52 \text{ s}, 0.56 \text{ s}, 0.57 \text{ s}, 0.54 \text{ s}$ and $0.59 \text{ s}$. The least count of the watch used for the measurement of time period is $0.01 \text{ s}$. Which of the following statement$(s)$ is(are) true?
$(A)$ The error in the measurement of $r$ is $10 \%$
$(B)$ The error in the measurement of $T$ is $3.57 \%$
$(C)$ The error in the measurement of $T$ is $2 \%$
$(D)$ The error in the determined value of $g$ is $11 \%$

If $f = x^2$,what is the relative error in $f$?

The mass of the body is $10.000\,g$ and its volume is $10.00\,cm^3$. If the measured values are expressed up to the correct significant figures,the maximum error in the measurement of density is

Why should the measurement of physical quantities with large exponents in an experiment be taken with high precision?