$A$ student in the laboratory measures the thickness of a wire using a screw gauge. The readings are $1.22\,mm$,$1.23\,mm$,$1.19\,mm$,and $1.20\,mm$. The percentage error is $\frac{x}{121}\%$. The value of $x$ 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:

$A$ 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

We can reduce random errors by

If $1 \%$ and $2 \%$ are the errors in the measurement of mass and density of a cube respectively,then the error in the measurement of length is (in $\%$)

The period of an oscillating simple pendulum is $T = 2 \pi \sqrt{\frac{\ell}{g}}$,where the length $\ell = 100 \text{ cm}$ with an error of $1 \text{ mm}$. The period $T = 2 \text{ s}$. The time for $100$ oscillations is measured by a stopwatch with a least count of $0.1 \text{ s}$. The percentage error in the gravitational acceleration $g$ is: (in $\%$)