Measure of two quantities along with the precision of respective measuring instrument $A = 2.5\,m{s^{ - 1}} \pm 0.5\,m{s^{ - 1}}$, $B = 0.10\,s \pm 0.01\,s$ The value of $AB$ will be
$\left( {0.25 \pm 0.08} \right)\,m$
$\left( {0.25 \pm 0.5} \right)\,m$
$\left( {0.25 \pm 0.05} \right)\,m$
$\left( {0.25 \pm 0.135} \right)\,m$
Write rule for error in result due to multiplication and division.
In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,\,kg\,$ and $(0.10 \pm 0.01)\,\,m\,$ respectively. The error in the measurement of density 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)
In order to determine the Young's Modulus of a wire of radius $0.2\, cm$ (measured using a scale of least count $=0.001\, cm )$ and length $1 \,m$ (measured using a scale of least count $=1\, mm$ ), a weight of mass $1\, kg$ (measured using a scale of least count $=1 \,g$ ) was hanged to get the elongation of $0.5\, cm$ (measured using a scale of least count $0.001\, cm$ ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)
A physical quantity $P$ is related to four observables $a, b, c$ and $d$ as follows: $P=\frac{a^{2} b^{2}}{(\sqrt{c} d)}$ The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 4 \%$ and $2 \%$ respectively. What is the percentage error in the quantity $P$ ? If the value of $P$ calculated using the above relation turns out to be $3.763,$ to what value should you round off the result?