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.

If $a, b, c$ are the percentage errors in the measurement of $A, B$ and $C$, then the percentage error in $ABC$ would be approximately

Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is

The dimensional formula for a physical quantity $x$ is $\left[ M ^{-1} L ^{3} T ^{-2}\right]$. The errors in measuring the quantities $M , L$ and $T$ respectively are $2 \%, 3 \%$ and $4 \%$. The maximum percentage of error that occurs in measuring the quantity $x$ is

A scientist performs an experiment in order to measure a certain physical quantity and takes $100$ observations. He repeats the same experiment and takes $400$ observations. By doing so,

The following observations were taken for determining surface tension $T$ of water by capillary method:

diameter of capillary, $D= 1.25 \times 10^{-2}\; m$

rise of water, $h=1.45 \times 10^{-2}\; m $ 

Using $g= 9.80 \;m/s^2$ and the simplified relation $T = \frac{{rhg}}{2}\times 10^3 N/m$ , the possible error in surface tension is ........... $\%$