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Energy $(E)$ , angular momentum $(L)$ and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

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Important Questions on Units and Measurements

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?

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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:

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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

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

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)

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

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?

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:

EASY

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

If $E$ and $E_{0}$ represent the energies, $t$ and $t_{0}$ represent the times, in which of the following is dimensionally correct relation?

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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:

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?

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

The dimensions of self or mutual inductance are given as

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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

HARD

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

x, v and a

denote the displacement, velocity and acceleration of a particle respectively executing SHM of periodic time

t

, then which one of the following does not change with time?

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

If force

(F),

velocity

(V)

and time

(T)

are taken as fundamental units, the dimensions of mass are

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

The dimension of stopping potential

V_{0}

in photoelectric effect in units of Planck’s constant

h

, speed of light

c

and Gravitational constant

G

and ampere

A

is:

HARD

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

A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation

(T)

of the liquid drop depends on radius

(r)

of the drop, density

(ρ)

and surface tension

(S)

of the liquid. Which among the following will be a possible expression for

T

(where,

k

is a dimensionless constant )?

EASY

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

A gas satisfies the relation

P V^{5 / 3} = K

where

P

is pressure,

V

is volume and

K

is constant. The dimensions of constant

K

are

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:

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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

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

Energy E, angular momentum L and universal gravitational constant G are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant h is

Important Questions on Units and Measurements

Learn and Prepare for any exam you want !

Energy $(E)$ , angular momentum $(L)$ and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is