Thickness of a pencil measured by using a screw gauge (least count $0.001 \,cm$) comes out to be $0.802 \,cm$. The percentage error in the measurement is ........... $\%$

The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. What will be the maximum percentage error in the estimation of the kinetic energy obtained by measuring mass and speed?

The percentage error in the measurement of $g$ is $.....\%$ (Given that $g = \frac{4 \pi^2 L}{T^2}$,$L = (10 \pm 0.1) \, cm$,$T = (100 \pm 1) \, s$)

$A$ scientist performs an experiment in order to measure a certain physical quantity and takes $100$ observations. He repeats the same experiment and takes $400$ observations. By doing so,

Calculate the mean percentage error in five observations: $80.0, 80.5, 81.0, 81.5, 82.0$. (in $\%$)

Two intervals of time are measured as $\Delta t_1 = (2.00 \pm 0.02) \ s$ and $\Delta t_2 = (4.00 \pm 0.02) \ s$. The value of $\sqrt{(\Delta t_1)(\Delta t_2)}$ with correct significant figures and error is