EASY

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Is Strain a dimensional constant?

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Important Questions on Physical World and Measurement

HARD

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and 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:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

S I

units, the dimensions of

\sqrt{\frac{ϵ_{0}}{μ_{0}}}

is:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

Dimensions of stress are:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Dimension and 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

μ_{0}

can be expressed in units of:

HARD

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

If energy

(E)

, velocity

(V)

and time

(T)

are chosen as the fundamental quantities, the dimensional formula of surface tension will be___(For surface tension, Force=Surface tension

\times

length)

EASY

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

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:

EASY

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

If momentum

(P)

, area

(A)

and time

(T)

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

MEDIUM

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

The quantities

x = \frac{1}{\sqrt{μ_{0} \in_{0}}}, y = \frac{E}{B}

and

z = \frac{l}{C R}

are defined where C-capacitance, R-Resistance,

ℓ -

length, E-Electric field, B-magnetic field and

\in 0, μ 0, -

free space permittivity and permeability respectively. Then:

EASY

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

The dimensional formula of

\sqrt{\frac{μ_{0}}{ε_{0}}}

EASY

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

Dimension of which base quantity corresponds to that

\sqrt{\frac{G h}{c^{3}}} = ?

EASY

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

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>Physical World and Measurement>Dimension and Dimensional Analysis

Expression for time in terms of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light) is proportional to:

MEDIUM

Physics>Mechanics>Physical World and Measurement>Dimension and Dimensional Analysis

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity

X

as follows:

[position] = [X^{α}];

[speed] = [X^{β}]

;

[acceleration] = [X^{p}]

;

[linear momentum] = [X^{q}]

;

[force] = [X^{r}]

. Then

Is Strain a dimensional constant?

Important Questions on Physical World and Measurement

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