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In the formula, $a = 3 b c^{2}$ , $a$ and $c$ have dimensions of electric capacitance and magnetic field intensity respectively. The dimensions of $b$ in $S . I .$ system are

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Important Questions on Units and Measurements

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:

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

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

S I

units, the dimensions of

\sqrt{\frac{ϵ_{0}}{μ_{0}}}

is:

MEDIUM

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

If dimensions of critical velocity,

v_{c}

of a liquid flowing through a tube are expressed as

[η^{x} ρ^{y} r^{z}]

, where,

η, ρ

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

z

are given by

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

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:

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

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 beaker contains a fluid of density

ρ

\frac{k g}{m^{3}}

, specific heat

S \frac{J}{k g^{o} C}

and viscosity

η

. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area

(\frac{\dot{Q}}{A})

by convection when beaker is put on a hot plate, a student proposes that it should depend on

η

(\frac{S Δ θ}{h})

and

(\frac{1}{ρ g})

when

Δ θ

(

{i n}^{o} C

) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for

(\frac{\dot{Q}}{A})

is:

MEDIUM

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

If force

(F),

velocity

(V)

and time

(T)

are taken as fundamental units, the dimensions of mass are

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:

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?

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?

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

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

The dimensions of self or mutual inductance are given as

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

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

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:

In the formula, a=3bc2, a and c have dimensions of electric capacitance and magnetic field intensity respectively. The dimensions of b in S.I. system are

Important Questions on Units and Measurements

Learn and Prepare for any exam you want !

In the formula, $a = 3 b c^{2}$ , $a$ and $c$ have dimensions of electric capacitance and magnetic field intensity respectively. The dimensions of $b$ in $S . I .$ system are