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 ......... $\%$.

We measure the period of oscillation of a simple pendulum. In successive measurements,the readings turn out to be $2.63 \;s, 2.56 \;s, 2.42 \;s, 2.71 \;s$,and $2.80 \;s$. Calculate the absolute errors,relative error,and percentage error.

$A$ physical quantity $P$ is related to four observations $a, b, c$ and $d$ as follows: $P = \frac{a^3 b^2}{c \sqrt{d}}$. The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 2 \%$ and $4 \%$ respectively. The percentage error in the quantity $P$ is: (in $\%$)

In an experiment for determination of the focal length of a thin convex lens,the distance of the object from the lens is $10 \pm 0.1 \text{ cm}$ and the distance of its real image from the lens is $20 \pm 0.2 \text{ cm}$. The error in the determination of focal length of the lens is $n \%$. The value of $n$ is. . . . . . .

The time period of a simple harmonic oscillator is $T = 2 \pi \sqrt{\frac{m}{k}}$. The measured value of mass $(m)$ of the object is $10 \ g$ with an accuracy of $10 \ mg$, and the time for $50$ oscillations of the spring is found to be $60 \ s$ using a watch of $2 \ s$ resolution. The percentage error in the determination of the spring constant $(k)$ is . . . . . . %.

$A$ capacitor of capacitance $(4.0 \pm 0.2) \mu F$ is charged to a potential of $(10.0 \pm 0.1) V$. The charge on the capacitor is