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Which of the following is an expression for energy in terms of the Planck's constant $h$ , the velocity of light $c$ , and the Gravitational constant $G$ ?

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Important Questions on Units and Measurements

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

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 Analysis and Its Applications

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>Units and Measurements>Dimensional Analysis and Its Applications

x, v

and

a

denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period

T

, then which of the following do not change with time?

EASY

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

Using dimensional analysis the resistivity in terms of fundamental constants

h, m_{e}, c, e & ε_{0}

can be expressed as

HARD

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

Young - Laplace law states that the excess pressure inside a soap bubble of radius

R

is given by

∆ P = \frac{4 σ}{R}

where

σ

is the coefficient of surface tension of the soap. The

E \overset{. .}{o} tv \overset{. .}{o} s

number

E_{0}

is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of the acceleration due to gravity

(g)

, the density of the surrounding fluid

(ρ)

and a characteristic length scale

(L)

which could be the radius of the bubble. A possible expression for

E_{0}

is:

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

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 Analysis and Its Applications

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]:

EASY

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

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:

HARD

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

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 Analysis and Its Applications

A neutron star with magnetic moment of magnitude

m

is spinning with angular velocity

ω

about its magnetic axis. The electromagnetic power P radiated by its is given by

μ_{0}^{x} m^{y} ω^{2} c^{u},

where

μ_{n}

and

c

are the permeability and speed of light in free space, respectively. Then

EASY

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

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

MEDIUM

Physics>Mechanics>Units and Measurements>Dimensional Analysis and Its Applications

Expression for time in terms of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light) is proportional to:

Which of the following is an expression for energy in terms of the Planck's constant h, the velocity of light c, and the Gravitational constant G?

Important Questions on Units and Measurements

Learn and Prepare for any exam you want !

Which of the following is an expression for energy in terms of the Planck's constant $h$ , the velocity of light $c$ , and the Gravitational constant $G$ ?