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If $Q= \frac{X^n}{Y^m}$ and $\Delta X$ is absolute error in the measurement of $X,$ $\Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ 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)
A physical quantity is given by $X = {M^a}{L^b}{T^c}$. The percentage error in measurement of $M,L$ and $T$ are $\alpha ,\beta $ and $\gamma $ respectively. Then maximum percentage error in the quantity X is
If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then
The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is
A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called time constant $(\tau )$. Dimensionally $\tau $ can be represented by
Two full turns of the circular scale of screw gauge cover a distance of $1\,mm$ on scale. The total number of divisions on circular scale is $50$. Further, it is found that screw gauge has a zero error of $+0.03\,mm$. While measuring the diameter of a thin wire a student notes the main scale reading of $3\,mm$ and the number of circular scale division in line, with the main scale is $35$. The diameter of the wire is .......... $mm$