EASY

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Turpentine oil is flowing through a capillary tube of length $l$ and radius r. The pressure difference between the two ends of the tube is p. The viscosity of oil is given by: $η = \frac{p (r^{2} - x^{2})}{4 v l}$ .

Here v is the velocity of oil at a distance x from the axis of the tube. From this relation, the dimensional formula of $η$ is -

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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

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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:

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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}

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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

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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 _________

EASY

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)

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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?

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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)

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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]:

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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-

Important Questions on Some Basic Concepts of Chemistry

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