In an experiment,the following observations were recorded: $L = 2.820 \, m, M = 3.00 \, kg, l = 0.087 \, cm$,Diameter $D = 0.041 \, cm$. Taking $g = 9.81 \, m/s^2$ and using the formula $Y = \frac{4MgL}{\pi D^2 l}$,the maximum permissible error in $Y$ is ......... $\%$.

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

To estimate $g$ from $g=4 \pi^2 \frac{L}{T^2}$,the error in the measurement of $L$ is $\pm 2 \%$ and the error in the measurement of $T$ is $\pm 3 \%$. The error in the estimated $g$ will be

The temperature of a body measured by a thermometer with a least count of $0.2 ^\circ C$ is $37.8 ^\circ C$. The temperature with error is represented as ... and the percentage error of the observation is ...

In the measurement of a physical quantity $X = \frac{A^2 B}{C^{1/3} D^3}$, the percentage errors introduced in the measurements of the quantities $A, B, C$, and $D$ are $2 \%, 2 \%, 4 \%$, and $5 \%$, respectively. Then, the minimum amount of percentage error in the measurement of $X$ is contributed by:

Time for $20$ oscillations of a pendulum is measured as $t_1 = 39.6\, s$,$t_2 = 39.9\, s$,and $t_3 = 39.5\, s$. What is the precision in the measurements? What is the accuracy of the measurement?