For $z=a^{2} x^{3} y^{\frac{1}{2}}$, where $a$ is a constant. If percentage error in measurement of $x$ and $y$ are $4 \%$ and $12 \%$, respectively, then the percentage error for $z$ will be $........... \%$

A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is

The radius of a sphere is $(5.3 \pm 0.1) \,cm$. The percentage error in its volume is

The acceleration due to gravity is measured on the surface of earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively, then percentage error in the measurement of acceleration due to gravity is ................ 

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,