If the random error in the arithmetic mean of $50$ observations is $\alpha$,then the random error in the arithmetic mean of $150$ observations would be

In five successive measurements, the mass of a ball is measured to be $2.61 \,g, 2.58 \,g, 2.40 \,g, 2.73 \,g$ and $2.80 \,g$. The mean absolute error in the measurement is (in $\,g$)

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 $11 \%$

The mass and volume of a body are found to be $(5.00 \pm 0.05) \ kg$ and $(1.00 \pm 0.05) \ m^3$ respectively. Then the maximum possible percentage error in its density is .......... $\%$

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

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