The maximum percentage error in the measurement of the density of a wire is: [Given: mass of wire $= (0.60 \pm 0.003) \ g$,radius of wire $= (0.50 \pm 0.01) \ cm$,length of wire $= (10.00 \pm 0.05) \ cm$]

$A$ current-carrying conductor obeys Ohm's law $(V = RI)$. If the current passing through the conductor is $I = (5 \pm 0.2) \text{ A}$ and the voltage developed is $V = (60 \pm 6) \text{ V}$,then find the percentage error in resistance $R$.

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 $11 \%$

An experiment measures quantities $a, b$ and $c$,and quantity $X$ is calculated from $X = ab^2 / c^3$. If the percentage errors in $a, b$ and $c$ are $\pm 1\%, \pm 3\%$ and $\pm 2\%$,respectively,then the percentage error in $X$ will be

$A$ body travels uniformly a distance of $(13.8 \pm 0.2) \ m$ in a time $(4.0 \pm 0.3) \ s$. The percentage error in velocity is ......... $\%$

$A$ physical quantity $A$ is related to four observables $a, b, c,$ and $d$ as follows: $A = \frac{a^2 b^3}{c \sqrt{d}}$. The percentage errors of measurement in $a, b, c,$ and $d$ are $1\%, 3\%, 2\%,$ and $2\%$ respectively. What is the percentage error in the quantity $A$?