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

Two capacitors with capacitance values $C_1 = 2000 \pm 10 \text{ pF}$ and $C_2 = 3000 \pm 15 \text{ pF}$ are connected in series. The voltage applied across this combination is $V = 5.00 \pm 0.02 \text{ V}$. The percentage error in the calculation of the energy stored in this combination of capacitors is . . . . . .

The percentage errors in measurements of mass and speed of a body are $2 \%$ and $3 \%$ respectively. What is the percentage error in kinetic energy of the body (in $\%$)?

The resistance of a wire is determined by measuring the current flowing through it and the voltage difference across its ends. If the percentage error in the measurement of current and voltage difference is $3\%$ each,what will be the percentage error in the resistance of the wire?

$Assertion$ : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively,the percentage error in $K.E.$ is $5\%$.
$Reason$ : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$

During Searle's experiment,the zero of the Vernier scale lies between $3.20 \times 10^{-2} \text{ m}$ and $3.25 \times 10^{-2} \text{ m}$ of the main scale. The $20^{\text{th}}$ division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of $2 \text{ kg}$ is applied to the wire,the zero of the Vernier scale still lies between $3.20 \times 10^{-2} \text{ m}$ and $3.25 \times 10^{-2} \text{ m}$ of the main scale,but now the $45^{\text{th}}$ division of the Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is $2 \text{ m}$ and its cross-sectional area is $8 \times 10^{-7} \text{ m}^2$. The least count of the Vernier scale is $1.0 \times 10^{-5} \text{ m}$. The maximum percentage error in the Young's modulus of the wire is: