#### Chapters

Chapter 2: Physics and Mathematics

Chapter 3: Rest and Motion: Kinematics

Chapter 4: The Forces

Chapter 5: Newton's Laws of Motion

Chapter 6: Friction

Chapter 7: Circular Motion

Chapter 8: Work and Energy

Chapter 9: Centre of Mass, Linear Momentum, Collision

Chapter 10: Rotational Mechanics

Chapter 11: Gravitation

Chapter 12: Simple Harmonics Motion

Chapter 13: Fluid Mechanics

Chapter 14: Some Mechanical Properties of Matter

Chapter 15: Wave Motion and Waves on a String

Chapter 16: Sound Waves

Chapter 17: Light Waves

Chapter 18: Geometrical Optics

Chapter 19: Optical Instruments

Chapter 20: Dispersion and Spectra

Chapter 21: Speed of Light

Chapter 22: Photometry

#### H.C. Verma Concept of Physics Part-1 (2018-2019 Session) by H.C Verma

## Chapter 1: Introduction to Physics

#### Chapter 1: Introduction to Physics Exercise Short Answers solutions [Pages 8 - 9]

The metre is defined as the distance travelled by light in `1/(299,792,458)` second. Why didn't people choose some easier number such as `1/(300,000,000)` second? Why not 1 second?

What are the dimensions of volume of a cube of edge *a.*

What are the dimensions of volume of a sphere of radius *a?*

What are the dimensions of the ratio of the volume of a cube of edge *a* to the volume of a sphere of radius *a*?

Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a metre stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?

If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?

If two quantities have same dimensions, do they represent same physical content?

It is desirable that the standards of units be easily available, invariable, indestructible and easily reproducible. If we use foot of a person as a standard unit of length, which of the above features are present and which are not?

Suggest a way to measure the thickness of a sheet of paper.

Suggest a way to measure the distance between the sun and the moon.

#### Chapter 1: Introduction to Physics Exercise MCQ solutions [Page 9]

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

length, mass and velocity,

length, time and velocity,

mass, time and velocity,

length, time and mass.

A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then

n ∝ size of u

n ∝ u

^{2}n ∝ `sqrt (u)`

n ∝ `1/u`

Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, `[ x ] = M^a L^b T^c`. The quantity mass

can always be dimensionally represented in terms of L, T and x,

can never be dimensionally represented in terms of L, T and x,

may be represented in terms of L, T and x if a = 0,

may be represented in terms of L, T and x if a ≠ 0

A dimensionless quantity

never has a unit,

always has a unit,

may have a unit,

does not exist.

A unitless quantity

never has a non-zero dimension

always has a non-zero dimension

may have a non-zero dimension

does not exist

\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\]

The value of n is

0

-1

1

none of these.

#### Chapter 1: Introduction to Physics Exercise MCQ solutions [Page 9]

The dimensions ML^{−1} T^{−2} may correspond to

work done by a force

linear momentum

pressure.

energy per unit volume.

Choose the correct statements(s):

A dimensionally correct equation may be correct.

A dimensionally correct equation may be incorrect.

A dimensionally incorrect equation may be correct.

A dimensionally incorrect equation may be incorrect.

Choose the correct statements(s):

(a) All quantities may be represented dimensionally in terms of the base quantities.

(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.

(c) The dimensions of a base quantity in other base quantities is always zero.

(d) The dimension of a derived quantity is never zero in any base quantity.

#### Chapter 1: Introduction to Physics Exercise Exercise solutions [Pages 9 - 10]

Find the dimensions of linear momentum .

Find the dimensions of frequency .

Find the dimensions of pressure.

Find the dimensions of

(a) angular speed ω,

(b) angular acceleration *α*,

(c) torque τ and

(d) moment of interia *I*.

Some of the equations involving these quantities are \[\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}, \alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}, \tau = F . r \text{ and }I = m r^2\].

The symbols have standard meanings.

Find the dimensions of electric field E.

The relevant equations are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]

where F is force, q is charge, v is speed, I is current, and a is distance.

Find the dimensions of magnetic field B.

The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]

where F is force, q is charge, v is speed, I is current, and a is distance.

Find the dimensions of magnetic permeability \[\mu_0\]

The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]

where F is force, q is charge, v is speed, I is current, and a is distance.

Find the dimensions of electric dipole moment p .

The defining equations are p = q.d and M = IA;

where d is distance, A is area, q is charge and I is current.

Find the dimensions of magnetic dipole moment M.

The defining equations are p = q.d and M = IA;

where d is distance, A is area, q is charge and I is current.

Find the dimensions of Planck's constant h from the equation E = hv where E is the energy and v is the frequency.

Find the dimensions of the specific heat capacity c.

(a) the specific heat capacity c,

(b) the coefficient of linear expansion α and

(c) the gas constant R.

Some of the equations involving these quantities are \[Q = mc\left( T_2 - T_1 \right), l_t = l_0 \left[ 1 + \alpha\left( T_2 - T_1 \right) \right]\] and PV = nRT.

Taking force, length and time to be the fundamental quantities, find the dimensions of density .

Taking force, length and time to be the fundamental quantities, find the dimensions of pressure .

Taking force, length and time to be the fundamental quantities, find the dimensions of momentum.

Taking force, length and time to be the fundamental quantities, find the dimensions of energy.

Suppose the acceleration due to gravity at a place is 10 m/s^{2}. Find its value if cm/(minute)^{2}.

The average speed of a snail is 0 . 020 miles/ hour and that of a leopard is 70 miles/ hour. Convert these speeds in SI units.

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure

= hpg in usual symbols.

Express the power of a 100 watt bulb in CGS unit.

The normal duration of I.Sc. Physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies. 1 microcentury = 10^{−}^{6} × 100 years. How many microcenturies did you sleep yesterday?

The surface tension of water is 72 dyne/cm. Convert it in SI unit.

The kinetic energy K of a rotating body depends on its moment of inertia I and its angular speedω. Assuming the relation to be \[k = KI^0w^B\] where k is a dimensionless constant, find a and b. Moment of inertia of a sphere about its diameter is \[\frac{2}{5}M r^2\]

Theory of relativity reveals that mass can be converted into energy. The energy E so obtained is proportional to certain powers of mass m and the speed c of light. Guess a relation among the quantities using the method of dimensions.

Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are \[{\text{ML}}^2 \text{I}^{- 2} \text{T}^{- 3}\] and \[{\text{ML}}^2 \text{T}^{- 3} \text{I}^{- 1}\] respectively.

The frequency of vibration of a string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

Test if the following equation is dimensionally correct:

\[h = \frac{2S cos\theta}{\text{ prg }},\]

where h = height, S = surface tension, ρ = density, I = moment of interia.

Test if the following equation is dimensionally correct:

\[v = \sqrt{\frac{P}{\rho}},\]

where *v* = frequency, ρ = density, *P* = pressure,

Test if the following equation is dimensionally correct:

\[V = \frac{\pi P r^4 t}{8 \eta l}\]

where v = frequency, P = pressure, η = coefficient of viscosity.

Test if the following equation is dimensionally correct:

\[v = \frac{1}{2 \pi}\sqrt{\frac{mgl}{I}};\]

where h = height, S = surface tension, \[\rho\] = density, P = pressure, V = volume, \[\eta =\] coefficient of viscosity, v = frequency and I = moment of interia.

Let x and a stand for distance. Is

\[\int\frac{dx}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}\] dimensionally correct?

## Chapter 1: Introduction to Physics

#### H.C. Verma Concept of Physics Part-1 (2018-2019 Session) by H.C Verma

#### Textbook solutions for Class 12

## H.C. Verma solutions for Class 12 Physics chapter 1 - Introduction to Physics

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Concepts covered in Class 12 Physics chapter 1 Introduction to Physics are Fundamental Forces in Nature, Physics, Technology and Society, Concept of Physics, Scope and Excitement of Physics, Nature of Physical Laws.

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