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

Earn 100

The escape velocity for a planet depends upon gravitational constant $G$ , radius $R$ of the planet and also its density $ρ$ . Obtain the formula for escape velocity from dimensional velocity.

Important Questions on Dimensions of Physical Quantities and Dimensional Analysis

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 8

The density of a material in

C . G . S unit

8 g / {cm}^{3}

. In a system of units in which the unit of length is

5 cm

and the unit of mass is

20 g

, what is the density of the material?

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 9

From dimensional analysis show that the speed of sound in an elastic medium of modulus of elasticity

E

and density

ρ

is proportional to

\sqrt{\frac{E}{ρ}}

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 10

The period of revolution

(T)

of a planet moving around the sun in a circular orbit depends upon the radius

(r)

of the orbit, mass

(M)

of the sun and the gravitation constant

(G)

. Prove that

T^{2} \propto r^{3}

, from 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 11

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.

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

The escape velocity for a planet depends upon gravitational constant G, radius R of the planet and also its density ρ. Obtain the formula for escape velocity from dimensional velocity.

Important Questions on Dimensions of Physical Quantities and Dimensional Analysis

Learn and Prepare for any exam you want !

The escape velocity for a planet depends upon gravitational constant $G$ , radius $R$ of the planet and also its density $ρ$ . Obtain the formula for escape velocity from dimensional velocity.