What is the dimension of velocity gradient?

Important Questions on Physical World and Measurement

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

In the following $I$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity:

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

Planck's constant $\left(h\right)$, speed of light in a vacuum $\left(c\right)$ and Newton's gravitational constant $\left(G\right)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi {\epsilon }_0}$, where [$c$ is velocity of light, $G$ is universal constant of gravitation, $e$ is charge & ${\epsilon }_0$ is permittivity of free space]:

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

In $\mathrm{S}\mathrm{I}$ units, the dimensions of $\sqrt{\frac{{\mathrm{ϵ}}_0}{{\mathrm{\mu }}_0}}$ is:

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

If dimensions of critical velocity, $v_{\mathrm{c}}$ of a liquid flowing through a tube are expressed as $\left[{\mathrm{\eta }}^{\mathrm{x}}{\mathrm{\rho }}^{\mathrm{y}}{r}^{\mathrm{z}}\right]$, where, $\mathrm{\eta },\mathrm{ }\mathrm{\rho }$ and $r$ are the coefficient of viscosity of liquid, density of liquid and radius of the tube, respectively, then, the values of $x$, $y$ and $\text{z}$ are given by

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

If Surface tension$\left(\mathrm{S}\right)$, Moment of Inertia $\left(\mathrm{I}\right)$ and Planck's constant $\left(\mathrm{h}\right),$ were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

Time $\left(T\right)$, velocity $\left(C\right)$ and angular momentum $\left(h\right)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

The force $F$ acting on a body of density $d$ are related by the reflection $F=\frac{y}{\sqrt{d}}$ . The dimensions of $y$ are

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck's constant $h$ are taken as fundamental quantities, the permeability of vacuum ${\mu }_0$ can be expressed in units of:

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

A beaker contains a fluid of density $\rho$$\frac{kg}{m^3}$ , specific heat $S\frac{J}{k{g}^{o}C}$ and viscosity $\eta$ . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $\left(\frac{\dot{Q}}{A}\right)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta$ , $\left(\frac{S\mathrm{\Delta }\theta }{h}\right)$ and $\left(\frac{1}{\rho g}\right)$ when $\mathrm{\Delta }\theta$ ( ${\mathrm{i}\mathrm{n}}^{o}C$ ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $\left(\frac{\dot{Q}}{A}\right)$ is:

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

If force $\left(F\right),$velocity $\left(V\right)$ and time $\left(T\right)$ are taken as fundamental units, the dimensions of mass are

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

The density of a material in $\mathrm{SI}$ units is $128 \mathrm{kg}\mathrm{ }{\mathrm{m}}^{-3}.$ In certain units in which the unit of length is $25 \mathrm{cm}$ and the unit of mass is $50 \mathrm{g},$ the numerical value of density of the material is:

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

In the formula $\mathrm{X}=5\mathrm{Y}{\mathrm{Z}}^2$ , $\mathrm{X}$ and $\mathrm{Z}$ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of $\mathrm{Y}$ in SI units?

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

$A,B,C$, and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD=Cln\left(BD\right)$ holds true. Then which of the combination is not a meaningful quantity?

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

Which of the following combinations has the dimension of electrical resistance $({\mathrm{ϵ}}_0$ is the permittivity of vacuum and ${\mathrm{\mu }}_0$ is the permeability of vacuum)?

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

The ratio of the dimensions of Planck’s constant to that of moment of inertia is the dimension of

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

The dimensions of self or mutual inductance are given as

HARD

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

If energy $\left(\mathrm{E}\right)$, velocity $\left(\mathrm{V}\right)$ and time $\left(\mathrm{T}\right)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension$\times$length)

MEDIUM

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

Expression for time in terms of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light) is proportional to:

EASY

Physics>General Physics>Physical World and Measurement>Dimensional Analysis

Let $L, R, C$ and $V$ represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{L}{RCV}$ in $SI$ units will be: