The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1 \%, 2 \%$ and $3 \%$ respectively. The maximum percentage error in the detection of the dissipated heat will be

The radius ( $\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as

$\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}$

$\mathrm{R}=(100 \pm 10) \mathrm{ohm}$

$l=(15 \pm 0.2) \mathrm{cm}$

The percentage error in resistivity of the material of the wire is :

The International Avogadro Coordination project created the world's most perfect sphere using Silicon in its crystalline form. The diameter of the sphere is $9.4 \,cm$ with an uncertainty of $0.2 \,nm$. The atoms in the crystals are packed in cubes of side $a$. The side is measured with a relative error of $2 \times 10^{-9}$, and each cube has $8$ atoms in it. Then, the relative error in the mass of the sphere is closest to (assume molar mass of Silicon and Avogadro's number to be known precisely)

Explain Absolute Error, Relative Error and Percentage Error.

The following observations were taken for determining surface tension $T$ of water by capillary method:

diameter of capillary, $D= 1.25 \times 10^{-2}\; m$

rise of water, $h=1.45 \times 10^{-2}\; m $ 

Using $g= 9.80 \;m/s^2$ and the simplified relation $T = \frac{{rhg}}{2}\times 10^3 N/m$ , the possible error in surface tension is ........... $\%$

In an experiment, the percentage of error occurred in the measurment of physical quantities $A, B, C$ and $D$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. Then the maximum percentage of error in the measurement $X,$

where $X = \frac{{{A^2}{B^{\frac{1}{2}}}}}{{{C^{\frac{1}{3}}}{D^3}}}$, will be