EASY

Earn 100

Volume has a dimension of $[L^{- 3}]$ .

81.25% studentsanswered this correctly

Important Questions on Units and Measurements

HARD

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

In terms of potential difference

V

, electic current

I

, permittivity

ε_{0}

, permeability

μ_{0}

and speed of light

c

, the dimensionally correct equation(s) is (are)

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:

MEDIUM

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

A physical quantity of the dimensions of length that can be formed out of

c, G

and

\frac{e^{2}}{4 π ε_{0}}

, where [

c

is velocity of light,

G

is universal constant of gravitation,

e

is charge &

ε_{0}

is permittivity of free space]:

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:

MEDIUM

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

Expression for time in terms of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light) is proportional to:

EASY

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

A, B, C

, and

D

are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation

A D = C l n (B D)

holds true. Then which of the combination is not a meaningful quantity?

EASY

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

Time

(T)

, velocity

(C)

and angular momentum

(h)

are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be:

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)?

MEDIUM

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

The density of a material in

SI

units is

128 kg m^{- 3} .

In certain units in which the unit of length is

25 cm

and the unit of mass is

50 g,

the numerical value of density of the material is:

HARD

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

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)

MEDIUM

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

S I

units, the dimensions of

\sqrt{\frac{ϵ_{0}}{μ_{0}}}

is:

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 :

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

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

In the formula

X = 5 Y Z^{2}

X

and

Z

have dimensions of capacitance and magnetic field, respectively. What are the dimensions of

Y

in SI units?

MEDIUM

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

The dimensions of self or mutual inductance are given as

EASY

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

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

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

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

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?

Volume has a dimension of L-3.

Important Questions on Units and Measurements

Learn and Prepare for any exam you want !

Volume has a dimension of $[L^{- 3}]$ .