EASY

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What are dimensional constants?

Important Questions on Units and Measurements

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

S I

units, the dimensions of

\sqrt{\frac{ϵ_{0}}{μ_{0}}}

is:

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

The dimensions of Stefan-Boltzmann constant

σ

can be written in terms of Planck's constant

h

, Boltzmann constant

k_{B}

and the speed of light c as

σ = h^{α} {(k_{B})}^{β} c^{γ}

. Here

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

If Surface tension

(S)

, Moment of Inertia

(I)

and Planck's constant

(h),

were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

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

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

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

μ_{0}

can be expressed in units of:

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Which of the following combinations has the dimension of electrical resistance

(ϵ_{0}

is the permittivity of vacuum and

μ_{0}

is the permeability of vacuum)?

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

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:

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

If speed

V

, area

A

and force

F

are chosen as fundamental units, then the dimension of Young's modulus will be :

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Planck's constant

(h)

, speed of light in a vacuum

(c)

and Newton's gravitational constant

(G)

are three fundamental constants. Which of the following combinations of these has the dimension of length?

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Stoke's law states that the viscous drag force $F$ experienced by a sphere of radius $a$ a, moving with a speed $v$ through a fluid with coefficient of viscosity $η$ , is given by $F = 6 π η a v$ .

If this fluid is flowing through a cylindrical pipe of radius $r$ , length $l$ and a pressure difference of $P$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as, $\frac{V}{t} = k {(\frac{P}{l})}^{a} η^{b} r^{c}$ , where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are-

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

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:

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

A length - scale

(l)

depends on the permittivity

(ε)

of a dielectric material, Boltzmann constant

k_{B}

, the absolute temperature T, the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles, Which of the following expressions (s) for

l

is (are) dimensionally correct?

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Given,

B

is magnetic field induction, and

μ_{0}

is the magnetic permeability of vacuum. The dimension of

\frac{B^{2}}{2 μ_{0}}

is:

HARD

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Let us consider a system of units in which mass and angular momentum are dimensionless. If the length has a dimension of

L,

which of the following statement (s) is/are correct?

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

A quantity

x

is given by

(\frac{I F v^{2}}{W L^{4}})

in terms of moment of inertia

I

, force

F

, velocity

v

, work

W

and length

L

. The dimensional formula for

x

is same as that of :

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

If momentum

(P)

, area

(A)

and time

(T)

are taken to be the fundamental quantities then the dimensional formula for energy is :

HARD

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

The dimensions of the area A of a black hole can be written in terms of the universal gravitational constant G, its mass M and the speed of light c as

A = G^{α} M^{β} c^{7} .

Here-

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Let $[\in_{0}]$ denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

EASY

Physics>Mechanics>Units and Measurements>Dimensional Formulae and Equations

Let

L, R, C

and

V

represent inductance, resistance, capacitance and voltage, respectively. The dimension of

\frac{L}{R C V}

S I

units will be:

What are dimensional constants?

Important Questions on Units and Measurements

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