Units & measurements practice · Mixed difficulty

A quantity $f$ is given by $f = \sqrt {\frac{{h{c^5}}}{G}} ,$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck’s constant.
Dimension of $f$ is that of

If error in measurement of volume of a cube is $6 \%$ then percentage error in the measurement of its surface area is

Assertion: Mass, length and time are fundamental physical quantities.

Reason: They are independent of each other.

The area of a square is $5.29\mathrm{ }\,\,c{m^2}$. The area of 7 such squares taking into account the significant figures is

A force is represented by $F=a x^2+b t^{\frac{1}{2}}$
Where $x=$ distance and $t=$ time. The dimensions of $b^2 / a$ are:

If a book with many printing errors contains four different formulae for the displacement $y$ of a particle undergoing a certain periodic motion.
(1) $y=a \sin \frac{2 \pi t}{T}$
(2) $y=a \sin v T$
(3) $y=\frac{a}{T} \sin \frac{t}{a}$
(4) $y=(a \sqrt{2})\left(\sin \frac{2 \pi t}{T}+\cos \frac{2 \pi t}{T}\right)$
where $a$ is the maximum displacement of the particle, $v$ is the speed of particle, $T$ is the time period of motion. Then dimensionally

$\mu_0$ and $\varepsilon_0$ denote the magnetic permeability and electrical permittivity of free space, then the dimensions of $\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ are similar to

Oersted is a unit of

The dimensions of $\;\frac{a}{b}$ in the equation $p = \frac{{a\; - \;{t^2}}}{{bx}}$ where p is pressure, x is distance and t is time, are

How many amu would make up $1 \mathrm{~kg}?$

Lumen is the unit of

What is the dimension of Luminous flux?

If $x$ and $a$ stand for distance, then for what value of $n$ is the given equation dimensionally correct? The equation is $\int \frac{d x}{\sqrt{a^2-x^n}}=\sin ^{-1} \frac{x}{a}$

The number of significant figures in $q = 1.6 \times {10^{ - 19}}$ coulomb are

Which of the following is not a dimensionless quantity?

Which is dimensionless?

Statement-I: Dimensional analysis can give us the numerical value of proportionality constants that may appear in an algebraic expression.
Statement-II: Dimensional analysis make use of the fact that dimensions can be treated as algebraic quantities.

If e is the charge, V the potential difference, T the temperature, then the units of $\frac{{eV}}{T}$ are the same as that of

To determine refractive index of glass also using
a travelling microscope, minimum number of
readings required are

If $e$ is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck’s constant, the quantity $\frac{1}{{4\pi { \in _0}}}\frac{{{{\left| e \right|}^2}}}{{hc}}$ has dimensions of

A physical quantity A is related to four observables a,b,c and d as follows $\;A = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$ The percentage errors of measurement in a,b,c and d are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity A?

Parsec is a unit of

If E,M,L and G denote energy, mass, angular momentum and gravitational constant respectively, then the quantity $\left( {E{L^2}/{M^5}{G^2}} \right)$ has the dimensions of

The entropy of any system is given by $\mathrm{S = }{\mathrm{\alpha }^\mathrm{2}}\mathrm{\beta\,\, ln}\left[ {\frac{{\mathrm{\mu kR}}}{{\mathrm{J}{\mathrm{\beta }^\mathrm{2}}}}\, + \,3} \right]$ where, $\alpha$ and $\beta$ are the constants; $\mu ,\,J,\,k\,\,\mathrm{and}\,\,R$ are number of moles, mechanical equivalent of heat, Boltzmann constant and gas constant, respectively.
$\left[ {\mathbf{Take},\,\,\mathrm{S = }\frac{{\mathrm{dQ}}}{\mathrm{T}}\;\;} \right]$
Choose the incorrect option.

The ratio of the volume of the atom to the volume of the nucleus is of the order of

If force is proportional to square of velocity, then the dimensions of proportionality constant are

Unit of Stefan's constant is

SI unit of permittivity is

Planck’s constant has the dimensions (unit) of

The quantity having the same units in all systems of units is