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An explosion releasing energy $E$ occurs in a medium of density $ρ$ . This results in a spherical blast wave of radius $r$ . One can express the radius of the blast wave at time $t$ after the explosion in a form $r = k t^{α} E^{β} ρ^{γ}$ where $k$ is a dimensionless constant. Then the radial speed of the blast wave can be written as $v \propto t^{n}$ . The value of $n$ is

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Important Questions on Units and Measurements

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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]:

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

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:

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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?

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

If force

(F),

velocity

(V)

and time

(T)

are taken as fundamental units, the dimensions of mass 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

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:

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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

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

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 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:

MEDIUM

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

The dimensions of self or mutual inductance are given as

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?

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?

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

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

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?

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

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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:

Important Questions on Units and Measurements

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