$A$ wooden cubical block of mass $m = 20 \text{ kg}$ is measured within an error of $10 \text{ g}$. Its side length $l = 100 \text{ cm}$ is measured within an error of $1 \text{ mm}$. Then, the relative error in the measurement of its density is

The error in the measurement of force acting normally on a square plate is $3 \%$. If the error in the measurement of the side of the plate is $1 \%$, then the error in the determination of the pressure acting on the plate is (in $\%$)

$A$ student performs an experiment for the determination of $g = \frac{4 \pi^{2} \ell}{T^{2}}$. Given $\ell = 1 \, m$,the student commits an error of $\Delta \ell$. For $T$,the student measures the time of $n$ oscillations using a stopwatch with a least count of $\Delta T$ and commits a human error of $0.1 \, s$. For which of the following data will the measurement of $g$ be the most accurate?

$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$.
$Reason$ : The permissible error is calculated by the formula $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.

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:

In a simple pendulum experiment,the maximum percentage error in the measurement of length is $2\%$ and that in acceleration due to gravity $g$ is $4\%$. Then the maximum percentage error in determination of the time-period is