# HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 chapter 1 - Introduction to Physics [Latest edition]

## Chapter 1: Introduction to Physics

Short Answers [Pages 8 - 9]

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 1 Introduction to Physics Short Answers [Pages 8 - 9]

Short Answers | Q 1 | Page 8

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?

Short Answers | Q 2.1 | Page 8

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

Short Answers | Q 2.2 | Page 8

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

Short Answers | Q 2.3 | Page 8

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?

Short Answers | Q 3 | Page 9

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?

Short Answers | Q 4 | Page 9

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?

Short Answers | Q 5 | Page 9

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

Short Answers | Q 6 | Page 9

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?

Short Answers | Q 7.1 | Page 9

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

Short Answers | Q 7.2 | Page 9

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

MCQ [Page 9]

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 1 Introduction to Physics MCQ [Page 9]

MCQ | Q 1 | 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.

MCQ | Q 2 | Page 9

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 ∝  u2

• n ∝ sqrt (u)

• n ∝ 1/u

MCQ | Q 3 | Page 9

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

MCQ | Q 4 | Page 9

A dimensionless quantity

• never has a unit,

• always has a unit,

•  may have a unit,

•  does not exist.

MCQ | Q 5 | Page 9

A unitless quantity

• never has a non-zero dimension

• always has a non-zero dimension

• may have a non-zero dimension

• does not exist

MCQ | Q 6 | Page 9

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

• 0

• -1

• 1

• none of these.

MCQ [Page 9]

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 1 Introduction to Physics MCQ [Page 9]

MCQ | Q 1 | Page 9

The dimensions ML−1 T−2 may correspond to

• work done by a force

•  linear momentum

•  pressure.

•  energy per unit volume.

MCQ | Q 2 | Page 9

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.

MCQ | Q 3 | Page 9

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.

Exercise [Pages 9 - 10]

### HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 Chapter 1 Introduction to Physics Exercise [Pages 9 - 10]

Exercise | Q 1.1 | Page 9

Find the dimensions of linear momentum .

Exercise | Q 1.2 | Page 9

Find the dimensions of frequency .

Exercise | Q 1.3 | Page 9

Find the dimensions of pressure.

Exercise | Q 2 | Page 9

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.

Exercise | Q 3.1 | Page 10

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.

Exercise | Q 3.2 | Page 9

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.

Exercise | Q 3.3 | Page 10

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.

Exercise | Q 4.1 | Page 10

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.

Exercise | Q 4.2 | Page 10

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.

Exercise | Q 5 | Page 10

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

Exercise | Q 6 | Page 10

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.

Exercise | Q 7.1 | Page 10

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

Exercise | Q 7.2 | Page 10

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

Exercise | Q 7.3 | Page 10

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

Exercise | Q 7.4 | Page 10

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

Exercise | Q 8 | Page 10

Suppose the acceleration due to gravity at a place is 10 m/s2. Find its value if cm/(minute)2.

Exercise | Q 9 | Page 10

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.

Exercise | Q 10 | Page 10

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.

Exercise | Q 11 | Page 10

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

Exercise | Q 12 | Page 10

The normal duration of I.Sc. Physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies. 1 microcentury = 106 × 100 years. How many microcenturies did you sleep yesterday?

Exercise | Q 13 | Page 10

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

Exercise | Q 14 | Page 10

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  $\frac{2}{5}M r^2$

Exercise | Q 15 | Page 10

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.

Exercise | Q 16 | Page 10

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.

Exercise | Q 17 | Page 10

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.

Exercise | Q 18.1 | Page 10

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.

Exercise | Q 18.2 | Page 10

Test if the following equation is dimensionally correct:
$v = \sqrt{\frac{P}{\rho}},$

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

Exercise | Q 18.3 | Page 10

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.

Exercise | Q 18.4 | Page 10

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.

Exercise | Q 19 | Page 10

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?

## HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 chapter 1 - Introduction to Physics

HC Verma solutions for Class 11, Class 12 Concepts of Physics Vol. 1 chapter 1 (Introduction to Physics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11, Class 12 Concepts of Physics Vol. 1 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11, Class 12 Concepts of Physics Vol. 1 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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