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 $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. 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 $11 \%$

The resistance $R =\frac{V}{I}$ where $V= 100  \pm 5 \,volts$ and $ I = 10  \pm 0.2$ amperes. What is the total error in $R$ ......... $\%$

The maximum percentage errors in the measurement of mass $(M)$, radius $(R)$ and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percentage error in the measurement of its angular momentum $(J=I \omega)$ about geometrical axis.

Quantity $Z$ varies with $x$ and $y$ , according to given equation $Z = x^2y - xy^2$ , where $x = 3.0 \pm 0.1$ and $y = 2.0 \pm 0.1$ . The value of $Z$ is 

Explain effect of multiplication or division of error on final result.

A physical quantity $X$ is given by $X = \frac{{2{k^3}{l^2}}}{{m\sqrt n }}$ The percentage error in the measurements of $k,\,l,\, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$