If h and e respectively represent Planck's constant and electronic charge, then find the dimension of h e and identify the physical quantity it corresponds to.

M L 2 T - 2 A - 1 ;Magnetic flux Given Planck's constant h and electric charge e Dimensions of Planck's constant h = energy frequency = ML 2 T - 2 T - 1 = ML 2 T - 1 Dimensions of charge = charge = current × time = AT Therefore h e = ML 2 T - 1 AT = ML 2 T - 2 A - 1 Now magnetic flux = ϕ = W q dt , where W = work done Hence, the dimensions of the magnetic flux= ϕ = ML 2 T 2 AT = ML 2 T - 2 A - 1 Thus h e = magnetic flux (dimensionally)

HARD

11th West Bengal Board

IMPORTANT

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If the velocity of light $(c)$ , gravitational constant $(G)$ and Planck's constant $(h)$ are chosen as fundamental units, find the dimensions of time in the new system.

Important Questions on Dimensions of Physical Quantities and Dimensional Analysis

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 12

h

and

e

respectively represent Planck's constant and electronic charge, then find the dimension of

(\frac{h}{e})

and identify the physical quantity it corresponds to.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 13

L, R, C

and

v

respectively represent inductance, resistance, capacitance and potential difference, then show that the dimensions of

\frac{L}{R C V}

are the same as those of

{(current)}^{- 1}

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 14

In a system of units in which the unit of mass is

{}^{'}a^{'}

kg, unit of length is

{}^{'}b^{'}

metre and the unit of time is

{}^{'}c^{'}

second find the magnitude of a calorie in this system.

HARD

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 15

To find the distance

d

over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density

ρ

of the fog, intensity (power/area)

s

of the light from the signal and its frequency

f

. The engineer finds that

d

is proportional to

\frac{1}{n}

. Find the value of

n

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 1

Out of the following pairs, which one does not have identical dimensions?

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 2

Identify the pair whose dimensions are equal.

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 3

Velocity of a particle at an instant

{}^{'}t^{'}

is given by

v = a t + b t^{2}

The dimension of

b

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 2 - Dimensions of Physical Quantities and Dimensional Analysis>EXERCISE>Q 4

Which two of the following five physical parameters have same dimensions? (i) energy density (ii) refractive index (iii) dielectric constant (iv) Young's modulus (v) magnetic field

If the velocity of light c, gravitational constant G and Planck's constant h are chosen as fundamental units, find the dimensions of time in the new system.

Important Questions on Dimensions of Physical Quantities and Dimensional Analysis

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If the velocity of light $(c)$ , gravitational constant $(G)$ and Planck's constant $(h)$ are chosen as fundamental units, find the dimensions of time in the new system.