The temperature of two bodies measured by a thermometer are $t_1 = 20\, ^oC + 0.5\, ^oC$ and $t_2 = 50\,^oC + 0.5\, ^oC$. The temperature difference and the error there in is

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

In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is

$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$

A physical quantity $z$ depends on four observables $a,$ $b,$ $c$ and $d ,$ as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is$......\%$

Write rule for error in result due to multiplication and division.

According to Joule's law of heating, heat produced $H = {I^2}\,Rt$, where I is current, $R$ is resistance and $t$ is time. If the errors in the measurement of $I, R$ and t are $3\%, 4\% $ and $6\% $ respectively then error in the measurement of $H$ is