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Identify the pair whose dimensions are equal –

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Important Questions on Some Basic Concepts of Chemistry

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Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Which of the following have same number of significant figures?
(A)

0.00253

(B)

1.0003

(C)

15.0

(D)

163

Choose the correct answer from the options given below

MEDIUM

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Expression for time in terms of

G

(universal gravitational constant),

h

(Planck constant) and

c

(speed of light) is proportional to:

MEDIUM

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

The number of significant figures in

50000.020 \times 10^{- 3}

MEDIUM

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Using dimensional analysis the resistivity in terms of fundamental constants

h, m_{e}, c, e & ε_{0}

can be expressed as

MEDIUM

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

The number of significant figures in

0.00340

is _________

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Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

The number of significant figures in

4.023

HARD

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Which two of the following quantities are dimensionally equivalent?

(i) Force
(ii) Pressure
(iii) Young's Modulus
(iv) Energy

EASY

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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:

EASY

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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:

HARD

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Planck' constant

h

, speed of light

c

and gravitational constant

G

are used to form a unit of length

L

and a unit of mass

M

. Then the correct option(s) is (are)

MEDIUM

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

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

Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Using the rules for significant figures, the correct answer for the expression

\frac{0.02858 \times 0.112}{0.5702}

will be:

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Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Among the following, the correct statement is :

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Chemistry>Physical Chemistry>Some Basic Concepts of Chemistry>Uncertainty in Measurement

Three successive measurements in an experiment gave the values 10.9, 11.4042 and 11.42. The correct way of reporting the average value is-

Identify the pair whose dimensions are equal –

Important Questions on Some Basic Concepts of Chemistry

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