Chapterwise Topicwise

Solved Papers
2021-1979

IITJEE
JEE Main & Advanced

Physics
DC Pandey

Arihant Prakashan (Series), Meerut


Arihant Prakashan (Series), Meerut
All Rights Reserved

© Author

Administrative & Production Offices
Regd. Office
‘Ramchhaya’ 4577/15, Agarwal Road, Darya Ganj, New Delhi -110002
Tele: 011- 47630600, 43518550

Head Office
Kalindi, TP Nagar, Meerut (UP) - 250002, Tel: 0121-7156203, 7156204

Sales & Support Offices
Agra, Ahmedabad, Bengaluru, Bareilly, Chennai, Delhi, Guwahati,
Hyderabad, Jaipur, Jhansi, Kolkata, Lucknow, Nagpur & Pune.

ISBN 978-93-25796-15-7
PO No : TXT-XX-XXXXXXX-X-XX
Published by Arihant Publications (India) Ltd.
For further information about the books published by Arihant, log on to
www.arihantbooks.com or e-mail at
Follow us on


Preface
Dear students it gives me immense pleasure to present this book in a new format.
I have been a part of the education sector for more than 25 years. I have observed
that IIT-JEE problems are really good and conceptual (except 1%). Most of our teaching
fraternity have developed our concepts from these problems.
But there has always existed a confusion amongst the students, about "how to
segregate the problems which need to be practiced before and after JEE Mains?"
I was also with this question many times but could not spare time to segregate them.
But now I used this lockdown period as an opportunity to upgrade my book and now
it's more student friendly. To extract best out of my book, it is divided into following
three parts.
l

Section 1 problems be attempted before JEE Mains

l

Section 2 problems be attempted after JEE Mains and

l


Section 3 problems consisting of above mentioned 1% problems. Students can
skip this section.

I have tried my level best to keep errors out of this book. A special note of thanks is
due to Mr. Anoop Dhyani for their special contribution. I shall be highly grateful to the
readers who point out any errors in my mail id :

Thanks and Regards
DC Pandey

Dedication
This book is dedicated to my honourable grandfather

(Late) Sh. Pitamber Pandey
(a Kumaoni poet; resident of village Dhaura (Almora) Uttarakhand)


CONTENTS
1.

General Physics

1-20

2.

Kinematics

21-36


3.

Laws of Motion

37-55

4.

Work, Power and Energy

56-70

5.

Centre of Mass

71-94

6.

Rotation

7.

Gravitation

134-147

8.


Simple Harmonic Motion

148-166

9.

Properties of Matter

167-193

10.

Wave Motion

194-223

11.

Heat and Thermodynamics

224-282

12.

Optics

283-346

13.


Current Electricity

347-378

14.

Electrostatics

379-438

15.

Magnetics

439-483

16.

Electromagnetic Induction and Alternating Current

484-517

17.

Modern Physics

518-584

JEE Advanced Solved Paper 2020
JEE Advanced Solved Paper 2021


585-598
1-16

95-133


SYLLABUS
JEE MAIN
SECTION A (80% weightage)
UNIT I Physics and Measurement
Physics, technology and society, SI units,
Fundamental and derived units. Least count,
accuracy and precision of measuring instruments,
Errors in measurement, Significant figures.
Dimensions of Physical quantities, dimensional
analysis and its applications.

UNIT II Kinematics
Frame of reference. Motion in a straight line: Positiontime graph, speed and velocity. Uniform and nonuniform motion, average speed and instantaneous
velocity.
Uniformly accelerated motion, velocity-time, position
time graphs, relations for uniformly accelerated
motion.
Scalars and Vectors, Vector addition and Subtraction,
Zero Vector, Scalar and Vector products, Unit Vector,
Resolution of a Vector. Relative Velocity, Motion in a
plane, Projectile Motion, Uniform Circular Motion.

UNIT III Laws of Motion

Force and Inertia, Newton's First Law of motion;
Momentum, Newton's Second Law of motion;
Impulse; Newton's Third Law of motion. Law of
conservation of linear momentum and its
applications, Equilibrium of concurrent forces. Static
and Kinetic friction, laws of friction, rolling friction.

Potential energy of a spring, conservation of
mechanical energy, conservative and
nonconservative forces; Elastic and inelastic
collisions in one and two dimensions.

UNIT V Rotational Motion
Centre of mass of a two-particle system, Centre of
mass of a rigid body; Basic concepts of rotational
motion; moment of a force, torque, angular
momentum, conservation of angular momentum
and its applications; moment of inertia, radius of
gyration. Values of moments of inertia for simple
geometrical objects, parallel and perpendicular axes
theorems and their applications.
Rigid body rotation, equations of rotational motion.

UNIT VI Gravitation
The universal law of gravitation.
Acceleration due to gravity and its variation with
altitude and depth.
Kepler's laws of planetary motion.
Gravitational potential energy; gravitational
potential.

Escape velocity. Orbital velocity of a satellite.
Geo-stationary satellites.

UNIT VII Properties of Solids & Liquids

Dynamics of uniform circular motion: Centripetal
force and its applications.

Elastic behaviour, Stress-strain relationship, Hooke's.
Law, Young's modulus, bulk modulus, modulus of
rigidity.

UNIT IV Work, Energy and Power

Pressure due to a fluid column; Pascal's law and its
applications.

Work done by a constant force and a variable force;
kinetic and potential energies, work-energy theorem,
power.

Viscosity, Stokes' law, terminal velocity, streamline
and turbulent flow, Reynolds number. Bernoulli's
principle and its applications.


Surface energy and surface tension, angle of contact,
application of surface tension - drops, bubbles and
capillary rise.


Electric field Electric field due to a point charge,
Electric field lines, Electric dipole, Electric field due to a
dipole, Torque on a dipole in a uniform electric field.

Heat, temperature, thermal expansion; specific heat
capacity, calorimetry; change of state, latent heat.

Electric flux, Gauss's law and its applications to find
field due to infinitely long, uniformly charged straight
wire, uniformly charged infinite plane sheet and
uniformly charged thin spherical shell.

Heat transfer-conduction, convection and radiation,
Newton's law of cooling.

UNIT VIII Thermodynamics
Thermal equilibrium, zeroth law of thermo-dynamics,
concept of temperature. Heat, work and internal
energy. First law of thermodynamics.
Second law of thermodynamics: reversible and
irreversible processes. Camot engine and its efficiency.

UNIT IX Kinetic Theory of Gases

Electric potential and its calculation for a point charge,
electric dipole and system of charges; Equipotential
surfaces, Electrical potential energy of a system of two
point charges in an electrostatic field.
Conductors and insulators, Dielectrics and electric
polarization, capacitor, combination of capacitors in

series and in parallel, capacitance of a parallel plate
capacitor with and without dielectric medium
between the plates, Energy stored in a capacitor.

Equation of state of a perfect gas, work done on
compressing a gas.

UNIT XII Current Electricity

Kinetic theory of gases - assumptions, concept of
pressure. Kinetic energy and temperature: rms speed
of gas molecules; Degrees of freedom, Law of
equipartition of energy, applications to specific heat
capacities of gases; Mean free path, Avogadro's
number.

Electric current, Drift velocity, Ohm's law, Electrical
resistance, Resistances of different materials, V-I
characteristics of Ohmic and nonohmic conductors,
Electrical energy and power, Electrical resistivity,
Colour code for resistors; Series and parallel
combinations of resistors; Temperature dependence
of resistance.

UNIT X Oscillations and Waves

Electric Cell and its Internal resistance, potential
difference and emf of a cell, combination of cells in
series and in parallel.


Periodic motion - period, frequency, displacement
as a function of time. Periodic functions. Simple
harmonic motion (S.H.M.) and its equation; phase;
oscillations of a spring - restoring force and force
constant; energy in S.H.M. - kinetic and potential
energies; Simple pendulum - derivation of expression
for its time period; Free, forced and damped
oscillations, resonance.
Wave motion. Longitudinal and transverse waves,
speed of a wave. Displacement relation for a
progressive wave. Principle of superposition of
waves, reflection of waves, Standing waves in strings
and organ pipes, fundamental mode and harmonics,
Beats, Doppler effect in sound.

UNIT XI Electrostatics
Electric charges Conservation of charge, Coulomb's
law-forces between two point charges, forces
between multiple charges; superposition principle
and continuous charge distribution.

Kirchhoff's laws and their applications. Wheatstone
bridge, Metre bridge.
Potentiometer - principle and its applications.

UNIT XIII Magnetic Effects of Current
and Magnetism
Biot-Savart law and its application to current carrying
circular loop. Ampere's law and its applications to
infinitely long current carrying straight wire and

solenoid. Force on a moving charge in uniform
magnetic and electric fields Cyclotron.
Force on a current-carrying conductor in a uniform
magnetic field. Force between two parallel currentcarrying conductors-definition of ampere. Torque
experienced by a current loop in uniform magnetic
field, Moving coil galvanometer, its current sensitivity
and conversion to ammeter and voltmeter.


Current loop as a magnetic dipole and its magnetic
dipole moment. Bar magnet as an equivalent solenoid,
magnetic field lines; Earth's magnetic field and
magnetic elements. Para, dia and ferro-magnetic
substances
Magnetic susceptibility and permeability, Hysteresis,
Electromagnets and permanent magnets.

Polarisation, plane polarized light; Brewster's law,
uses of plane polarized light and Polaroids.

UNIT XVII Dual Nature of Matter
and Radiation
Dual nature of radiation. Photoelectric effect,
Hertz and Lenard's observations; Einstein's
photoelectric equation; particle nature of light.

UNIT XIV Electromagnetic Induction
and Alternating Currents

Matter waves-wave nature of particle, de Broglie

relation. Davisson-Germer experiment.

Electromagnetic induction; Faraday's law, induced emf
and current; Lenz's Law, Eddy currents. Self and mutual
inductance.

UNIT XVIII Atoms and Nuclei

Alternating currents, peak and rms value of alternating
current/ voltage; reactance and impedance; LCR series
circuit, resonance; Quality factor, power in AC circuits,
wattless current.
AC generator and transformer.

UNIT XV Electromagnetic Waves
Electromagnetic waves and their characteristics.
Transverse nature of electromagnetic waves.
Electromagnetic spectrum (radio waves, microwaves,
infrared, visible, ultraviolet, X-rays, gamma rays).
Applications of e.m. waves.

UNIT XVI Optics
Reflection and refraction of light at plane and spherical
surfaces, mirror formula, Total internal reflection and
its applications, Deviation and Dispersion of light by a
prism, Lens Formula, Magnification, Power of a Lens,
Combination of thin lenses in contact, Microscope and
Astronomical Telescope (reflecting and refracting) and
their magnifying powers.
Wave optics wave front and Huygens' principle, Laws

of reflection and refraction using Huygen's principle.
Interference, Young's double slit experiment and
expression for fringe width, coherent sources and
sustained interference of light. Diffraction due to a
single slit, width of central maximum. Resolving
power of microscopes and astronomical telescopes,

Alpha-particle scattering experiment;
Rutherford's model of atom; Bohr model, energy
levels, hydrogen spectrum.
Composition and size of nucleus, atomic masses,
isotopes, isobars; isotones. Radioactivity-alpha,
beta and gamma particles/rays and their
properties; radioactive decay law. Mass-energy
relation, mass defect; binding energy per nucleon
and its variation with mass number, nuclear fission
and fusion.

UNIT XIX Electronic Devices
Semiconductors; semiconductor diode: I-V
characteristics in forward and reverse bias; diode
as a rectifier; I-V characteristics of LED,
photodiode, solar cell, and Zener diode; Zener
diode as a voltage regulator. Junction transistor,
transistor action, characteristics of a transistor
transistor as an amplifier (common emitter
configuration) and oscillator. Logic gates (OR, AND,
NOT, NAND & NOR). Transistor as a switch.

UNIT XX Communication Systems

Propagation of electromagnetic waves in the
atmosphere; Sky and space wave propagation,
Need for modulation, Amplitude and Frequency
Modulation, Bandwidth of signals, Bandwidth of
Transmission medium, Basic Elements of a
Communication System (Block Diagram only)


SECTION B (20% weightage)
UNIT XXI Experimental Skills
Familiarity with the basic approach and observations
of the experiments and activities
1. Vernier callipers - its use to measure internal and
external diameter and depth of a vessel
2. Screw gauge - its use to determine thickness/
diameter of thin sheet/wire.
3. Simple Pendulum - dissipation of energy by
plotting a graph between square of amplitude
and time.
4. Metre Scale - mass of a given object by principle
of moments
5. Young's modulus of elasticity of the material of a
metallic wire
6. Surface tension of water by capillary rise and
effect of detergents
7. Coefficient of Viscosity of a given viscous liquid
by measuring terminal velocity of a given
spherical body.
8. Plotting a cooling curve for the relationship
between the temperature of a hot body

and time.
9. Speed of sound in air at room temperature
using a resonance tube.
10. Specific heat capacity of a given (i) solid and (ii)
liquid by method of mixtures.
11. Resistivity of the material of a given wire using
metre bridge.
12. Resistance of a given wire using Ohm's law
13. Potentiometer

(i) Comparison of emf of two primary cells.
(ii) Determination of Internal resistance of a cell.
14. Resistance and figure of merit of a
galvanometer by half deflection method.
15. Focal length of
(i) Convex mirror
(ii) Concave mirror
(iii) Convex lens
Using parallax method.
16. Plot of angle of deviation vs angle of incidence
for a triangular prism.
17. Refractive index of a glass slab using a travelling
microscope
18. Characteristic curves of a p-n junction diode in
forward and reverse bias.
19. Characteristic curves of a Zener diode and
finding reverse break down voltage.
20. Characteristic curves of a transistor and finding
current gain and voltage gain.
21. Identification of Diode, LED, Transistor, IC,

Resistor, Capacitor from mixed collection of
such items.
22. Using multimeter to
(i) Identify base of a transistor
(ii) Distinguish between npn and pnp type
transistor
(iii) See the unidirectional flow of current in case
of a diode and an LED.
(iv) Check the correctness or otherwise of a
given electronic component (diode,
transistor or IC).


JEE ADVANCED
General
Units and dimensions, dimensional analysis, least count, significant figures, Methods of measurement and
error analysis for physical quantities pertaining to the following experiments, Experiments based on using
vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young's
modulus by Searle's method, Specific heat of a liquid using calorimeter, focal length of a concave mirror
and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm's law
using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post
office box.

Mechanics
Kinematics in one and two dimensions (Cartesian coordinates only), projectiles, Circular motion (uniform
and non-uniform), Relative velocity.
Newton's Laws of Motion, Inertial and uniformly accelerated frames of reference, Static and dynamic
friction, Kinetic and potential energy, Work and power, Conservation of linear momentum and mechanical
energy.
Systems of Particles, Centre of mass and its motion, Impulse, Elastic and inelastic collisions.

Law of Gravitation, Gravitational potential and field, Acceleration due to gravity, Motion of planets and
satellites in circular orbits, Escape velocity.
Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform
bodies with simple geometrical shapes, Angular momentum, Torque, Conservation of angular momentum,
Dynamics of rigid bodies with fixed axis of rotation, Rolling without slipping of rings, cylinders and
spheres, Equilibrium of rigid bodies, Collision of point masses with rigid bodies.
Linear and angular simple harmonic motions.
Hooke's law, Young's modulus.
Pressure in a fluid, Pascal's law, Buoyancy, Surface energy and surface tension, capillary rise, Viscosity
(Poiseuille's equation excluded), Stoke's law, Terminal velocity, Streamline flow, Equation of continuity,
Bernoulli's theorem and its applications.
Wave motion (plane waves only), longitudinal and transverse waves, Superposition of waves; progressive
and stationary waves, Vibration of strings and air columns. Resonance, Beats, Speed of sound in gases,
Doppler effect (in sound).


Thermal Physics
Thermal expansion of solids, liquids and gases, Calorimetry, latent heat, Heat conduction in one
dimension, Elementary concepts of convection and radiation, Newton's law of cooling, Ideal gas laws,
Specific heats (Cv and Cp for monatomic and diatomic gases), Isothermal and adiabatic processes,
bulk modulus of gases, Equivalence of heat and work, First law of thermodynamics and its
applications (only for ideal gases). Blackbody radiation, absorptive and emissive powers, Kirchhoff's
law, Wien's displacement law, Stefan's law.

Electricity and Magnetism
Coulomb's law, Electric field and potential, Electrical Potential energy of a system of point charges and
of electrical dipoles in a uniform electrostatic field, Electric field lines, Flux of electric field; Gauss's law
and its application in simple cases, such as, to find field due to infinitely long straight wire, uniformly
charged infinite plane sheet and uniformly charged thin spherical shell.
Capacitance, Parallel plate capacitor with and without dielectrics, Capacitors in series and parallel,

Energy stored in a capacitor.
Electric Current, Ohm's law, Series and parallel arrangements of resistances and cells, Kirchhoff's laws
and simple applications, Heating effect of current.
Biot-Savart law and Ampere's law, magnetic field near a current-carrying straight wire, along the axis
of a circular coil and inside a long straight solenoid, Force on a moving charge and on a currentcarrying wire in a uniform magnetic field.
Magnetic Moment of a Current Loop, Effect of a uniform magnetic field on a current loop, Moving coil
galvanometer, voltmeter, ammeter and their conversions.
Electromagnetic induction, Faraday's law, Lenz's law, Self and mutual inductance, RC, LR and LC
circuits with DC and AC sources.

Optics
Rectilinear propagation of light, Reflection and refraction at plane and spherical surfaces, Total
internal reflection, Deviation and dispersion of light by a prism, Thin lenses, Combinations of mirrors
and thin lenses, Magnification.
Wave Nature of Light, Huygen's principle, interference limited to Young's double-slit experiment.

Modern Physics
Atomic nucleus, Alpha, beta and gamma radiations, Law of radioactive decay, Decay constant, Half-life
and mean life, Binding energy and its calculation, Fission and fusion processes, Energy calculation in
these processes.
Photoelectric Effect, Bohr's theory of hydrogen-like atoms, Characteristic and continuous
X-rays, Moseley's law, de Broglie wavelength of matter waves.


1
General Physics
SECTION-1
Fill in the Blanks

9. A wire has a mass (0.3 ± 0.003) g, radius (0.5 ± 0.005) mm


1. Planck’s constant has dimensions ……… .

(1985)

2. In the formula X = 3YZ 2 , X and Z have dimensions of
capacitance and magnetic induction, respectively. The
dimensions of Y in MKSQ system are ……… .
(1988)

3. The dimensions of electrical conductivity is ……… .
(1997)

4. The equation of state of a real gas is given by

(1997)

(a) [ M 0 L2 T0 ]

where p , V and T are pressure, volume and temperature,
respectively and R is the universal gas constant. The
dimensions of the constant a in the above equation is …… .

Objective Questions I (Only one correct option)
5. In the formula X = 3Y Z 2 , X and Z have dimensions of
capacitance and magnetic induction, respectively. What are
the dimensions of Y in MKSQ system?
(1995)
(a) [ M –3 L–1 T3 Q4 ]
(b) [M –3 L–2 T4 Q4 ]

4

(c) [M L T Q ]

6. The dimensions of

αZ

α − kθ
e
p is pressure, Z is distance, k is
β
Boltzmann’s constant and θ is the temperature. The
dimensional formula of β will be

10. In the relation, p =

(2004)

a

 p + 2  (V − b ) = RT

V 

−2 −2 4

and length (6 ± 0.06 ) cm. The maximum percentage error in
the measurement of its density is
(2004)

(a) 1
(b) 2
(c) 3
(d) 4

(b) [ ML2 T] (c) [ ML0 T−1 ] (d) [ M 0 L2 T−1 ]

11. Which of the following sets have different dimensions?
(a) Pressure, Young’s modulus, Stress
(b) Emf, Potential difference, Electric potential
(c) Heat, Work done, Energy
(d) Dipole moment, Electric flux, Electric field

12. The circular scale of a screw gauge has 50 divisions and
pitch of 0.5 mm. Find the diameter of sphere. Main scale
reading is 2.
(2006)
AB

S

N H
2

–3 –2 4

(d) [ M L T Q]

(b) [ML2 T−2 ]


(c) [MLT−2 ]

(d) [ML2 T−1 ]

(2000)

−2

8. A cube has a side of length1.2 × 10 m. Calculate its volume.
(2003)

(b) 1.73 × 10−6 m3

(c) 1.70 × 10−6 m3

(d) 1.732 × 10−6 m3

K

M

(a) 1.2 mm

(b) 1.25 mm

(c) 2.20 mm

(d) 2.25 mm

13. A vernier calipers has 1 mm marks on the main scale. It has


∆V
7. A quantity X is given by ε 0 L
, where ε 0 is the
∆t
permittivity of free space, L is a length, ∆V is a potential
difference and ∆t is a time interval. The dimensional
formula for X is the same as that of
(2001)
(a) resistance (b) charge
(c) voltage
(d) current

(a) 1.7 × 10−6 m3

E
25

R

1
ε 0 E 2 (ε 0 : permittivity of free space;
2

E : electric field) is
(a) [MLT−1 ]

(2005)

20 equal divisions on the vernier scale which match with

16 main scale divisions. For this vernier calipers, the least
count is
(2010)
(a) 0.02 mm (b) 0.05 mm (c) 0.1 mm (d) 0.2 mm



14. In the determination of Young’s modulus Y =

4 MLg 
 by
πld 2 

using Searle’s method, a wire of length L = 2m and diameter
d = 0.5 mm is used. For a load M = 2.5 kg, an extension
l = 0.25 mm in the length of the wire is observed. Quantities
d and l are measured using a screw gauge and a micrometer,
respectively. They have the same pitch of 0.5 mm. The
number of divisions on their circular scale is 100. The


2 General Physics
δL
Then the percentage error in the measurement, , is closest
L (2017 Adv.)
to
(a) 1%
(b) 5%
(c) 3%
(d) 0.2%


contributions to the maximum probable error of the Y
measurement is
(2012)
(a) due to the errors in the measurements of d and l are the
same
(b) due to the error in the measurement of d is twice that
due to the error in the measurement of l
(c) due to the error in the measurement of l is twice that due
to the error in the measurement of d
(d) due to the error in the measurement of d is four times
that due to the error in the measurement of l

20. The density of a material in the shape of a cube is

15. Let [ ε 0 ] denote the dimensional formula of the permittivity

21. The pitch and the number of divisions, on the circular

of vacuum. If M = mass, L = length, T = Time and
(2013 Main)
A = electric current, then
(a) [ ε 0 ] = [ M−1 L−3 T2 A ]
(b) [ ε 0 ] = [ M −1 L−3 T4 A 2 ]
(c) [ ε 0 ] = [ M −2 L2 T−1 A −2 ]
(d) [ ε 0 ] = [ M

−1

2


−1

2

L T A ]

16. A student measured the length of a rod and wrote it as
3.50 cm. Which instrument did he use to measure it?
(a) A meter scale
(2014 Main)
(b) A vernier caliper where the 10 divisions in vernier scale
matches with 9 divisions in main scale and main scale has
10 divisions in 1 cm
(c) A screw gauge having 100 divisions in the circular scale
and pitch as 1 mm.
(d) A screw gauge having 50 divisions in the circular scale
and pitch as 1 mm.

17. The period of oscillation of a simple pendulum is
T = 2π

L
. Measured value of L is 20.0 cm known to 1 mm
g

accuracy and time for 100 oscillations of the pendulum is
found to be 90 s using a wrist watch of 1s resolution. The
accuracy in the determination of g is
(2015 Main)

(a) 3%
(b) 2%
(c) 1%
(d) 5%

18. A screw gauge with a pitch of 0.5 mm and a circular scale
with 50 divisions is used to measure the thickness of a thin
sheet of aluminium. Before starting the measurement, it is
found that when the two jaws of the screw gauge are brought
in contact, the 45th division coincides with the main scale
line and that the zero of the main scale is barely visible.
What is the thickness of the sheet, if the main scale reading
is 0.5 mm and the 25th division coincides with the main
scale line?
(2016 Main)
(a) 0.75 mm
(b) 0.80 mm
(c) 0.70 mm
(d) 0.50 mm

19. A person measures the depth of a well by measuring the time
interval between dropping a stone and receiving the sound
of impact with the bottom of the well. The error in his
measurement of time is δT = 0. 01 s and he measures the
depth of the well to be L = 20m. Take the acceleration due to
gravity g = 10 ms −2 and the velocity of sound is 300 ms −1 .

determined by measuring three sides of the cube and its
mass. If the relative errors in measuring the mass and length
are respectively 1.5% and 1% , the maximum error in

determining the density is
(2018 Main)
(a) 6%
(b) 2.5%
(c) 3.5%
(d) 4.5%
scale for a given screw gauge are 0.5 mm and 100,
respectively. When the screw gauge is fully tightened
without any object, the zero of its circular scale lies 3
divisions below the reference line.
The readings of the main scale and the circular scale for a
thin sheet are 5.5 mm and 48 respectively, the thickness of
this sheet is
(2019 Main)
(a) 5.950 mm (b) 5.725 mm (c) 5.755 mm (d) 5.740 mm

22. Which of the following combinations has the dimension of
electrical resistance (ε 0 is the permittivity of vacuum and µ 0
is the permeability of vacuum)?
(2019 Main)
µ0
µ0
ε0
ε
(a)
(b)
(c)
(d) 0
ε0
ε0

µ0
µ0

23. In the formula X = 5YZ 2 , X and Z have dimensions of
capacitance and magnetic field, respectively. What are the
dimensions of Y in SI units?
(2019 Main)
(b) [M− 2L0 T − 4A − 2 ]
(a) [M− 1L− 2 T 4A 2 ]
(c) [M− 3L− 2 T 8A 4 ]

(d) [M− 2L− 2 T 6A3 ]

24. If surface tension ( S ), moment of inertia ( I ) and Planck’s
constant ( h ), were to be taken as the fundamental units, the
dimensional formula for linear momentum would be
(2019 Main)

(a) S 1 / 2 I 1 / 2 h −1
(c) S 1 / 2 I 1 / 2 h 0

(b) S 3 / 2 I 1 / 2 h 0
(d) S 1 / 2 I 3 / 2 h −1

25. In SI units, the dimensions of

ε0
is
µ0


(a) [A −1TML3 ]

(b) [AT 2 M−1L−1 ]

(c) [AT −3 ML3/ 2 ]

(d) [A 2T 3 M−1L−2 ]

26. Let

l , r, c, and

resistance,
l
capacitance and voltage, respectively. The dimension of
rcv
in SI units will be
(2019 Main)
(a) [LT 2 ]
(b) [LTA]
(c) [A −1 ]
(d) [LA −2 ]
v

represent

(2019 Main)

inductance,


27. If speed (V ), acceleration ( A ) and force ( F ) are considered
as fundamental units, the dimension of Young’s modulus
will be
(2019 Main)
(a) [ V−4 A − 2 F]
(b) [ V−2 A 2 F2 ]
(c) [ V−2 A 2 F− 2 ]

(d) [ V−4 A 2 F]


General Physics 3
28. The force of interaction between two atoms is given by
 x2 
F = αβ exp  −
 ; where x is the distance, k is the
 αkT 
Boltzmann constant and T is temperature and α and β are two
constants. The dimension of β is
(2019 Main)
(a) [MLT −2 ] (b) [M0L2T −4] (c) [M2LT −4] (d) [M2L2T −2]
−3

29. The density of a material in SI units is 128 kg m . 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
(2019 Main)

(a) 40


(b) 16

(c) 640

(d) 410

37. Two vectors A and B

have equal magnitudes. The
magnitude of ( A + B ) is n times the magnitude of ( A − B ).
The angle between A and B is
(2019 Main)
2




n
−
1
n
−
1
(b) sin −1 
(a) sin −1  2


 n + 1
 n + 1


 n 2 − 1
(c) cos −1  2

 n + 1

38. In the cube of side ‘a’ shown in the figure, the vector from
the central point of the face ABOD to the central point of the
face BEFO will be
(2019 Main)

30. In form of G (universal gravitational constant), h (Planck

z

constant) and c (speed of light), the time period will be
proportional to
(2019 Main)
(a)

Gh
c5

5

(b)

hc
G

3


(c)

c
Gh

(d)

 n − 1
(d) cos −1 

 n + 1

B

Gh

E

A

c3

F

O

31. The area of a square is 5.29 cm 2 . The area of 7 such squares

y


taking into account the significant figures is
(2019 Main)

(a) 37.030 cm 2
(c) 37.03 cm 2

(b) 37.0 cm 2
(d) 37 cm 2

32. In the density measurement of a cube, the mass and edge
length are measured as (10.00 ± 010
. ) kg and ( 010
. ± 0.01) m,
respectively. The error in the measurement of density is
(2019 Main)

(a) 0.01 kg/m 3
(c) 0.07 kg/m 3

(b) 0.10 kg/m 3
(d) 0.31 kg/m 3

acceleration due to gravity ( g ), time taken for 20
oscillations is measured by using a watch of 1 second least
count. The mean value of time taken comes out to be 30 s.
The length of pendulum is measured by using a meter scale
of least count 1 mm and the value obtained 55.0 cm. The
percentage error in the determination of g is close to
(2019 Main)


(b) 6.8%

(c) 3.5%

(d) 0.2%

34. The diameter and height of a cylinder are measured by a

meter scale to be 12.6 ± 01
. cm and 34.2 ± 01
. cm,
respectively. What will be the value of its volume in
appropriate significant figures ?
(2019 Main)
(a) 4300 ± 80 cm 3
(b) 4260 ± 80 cm 3

(c) 4264.4 ± 81.0 cm 3

The minimum number of divisions on its circular scale
required to measure 5 µm diameter of a wire is
(2019 Main)

(b) 200
(d) 100

(b)

$)

k

39. Two forces P and Q of magnitude 2F and 3F, respectively

(2019 Main)

(a) 60°

(b) 120°

(c) 30°

(d) 90°

40. Using screw gauge of pitch 0.1 cm and 50 divisions on its
circular scale, the thickness of an object is measured. It
should correctly be recorded as
(2020 Main)
(a) 2.121 cm (b) 2.124 cm (c) 2.125 cm (d) 2.123 cm

Objective Questions II (One or more correct option)
41. L, C and R represent the physical quantities inductance,
capacitance and resistance, respectively. The combinations
which have the dimensions of frequency are
(1984)
1
R
1
C
(a)

(b)
(c)
(d)
RC
L
L
LC
following pairs are the same. Identify the pair (s).
(a) Torque and work
(b) Angular momentum and work
(c) Energy and Young’s modulus
(d) Light year and wavelength

(1986)

43. The pairs of physical quantities that have the same

36. Let | A1 | = 3, | A2 | = 5 and | A1 + A2 | = 5. The value of
( 2 A1 + 3 A 2 ) ⋅ ( 3 A1 − 2 A 2 ) is
(a) −106.5
(b) −112. 5
(c) −99.5
(d) −118. 5

1 $ $
a( j − i)
2
1 $ $
(d) a ( k
− i)

2

$)
k

42. The dimensions of the quantities in one (or more) of the

(d) 4264 ± 81 cm 3

35. The least count of the main scale of a screw gauge is 1 mm.

(a) 50
(c) 500

D

are at an angle θ with each other. If the force Q is doubled,
their resultant also gets doubled. Then, the angle θ is

33. In a simple pendulum, experiment for determination of

(a) 0.7%

x

1
(a) a ( $i −
2
1
(c) a ( $j −

2

(2019 Main)

dimensions is (are )
(a) Reynolds number and coefficient of friction
(b) Curie and frequency of a light wave
(c) Latent heat and gravitational potential
(d) Planck’s constant and torque

(1995)


4 General Physics
44. Let [ ε 0 ] denote the dimensional formula of the permittivity

50. The relation between [ ε 0 ] and [µ 0 ] is
(a) [µ 0 ] = [ ε 0 ] [L]2 [T]−2

of the vacuum and [µ 0 ] that of the permeability of the
vacuum. If M = mass, L = length, T = time and I = electric
current.
(1998)

(b) [µ 0 ] = [ ε 0 ] [L]−2 [T]2
(c) [µ 0 ] = [ ε 0 ]−1 [L]2 [T]−2

(a) [ ε 0 ] = [ M −1 L−3 T2 I]

(d) [µ 0 ] = [ ε 0 ]−1 [L]−2 [T]2


(b) [ ε 0 ] = [ M −1 L−3 T4 I2 ]
(c) [µ 0 ] = [ MLT−2 I−2 ]
(d) [µ 0 ] = [ ML T
2

−1

Match the Columns
51. Column I gives three physical quantities. Select the

I]

appropriate units for the choices given in Column II. Some
of the physical quantities may have more than one choice.

45. The SI unit of the inductance, the henry can by written as
(1998)

(a) weber/ampere
(c) joule/(ampere)2

(b) volt-second/ampere
(d) ohm-second

46. A student uses a simple pendulum of exactly 1m length to
determine g, the acceleration due to gravity. He uses a stop
watch with the least count of 1 s for this and records 40 s for
20 oscillations. For this observation, which of the following
statement(s) is/are true?

(2010)
(a) Error ∆T in measuring T, the time period, is 0.05 s
(b) Error ∆T in measuring T, the time period, is 1 s
(c) Percentage error in the determination of g is 5%
(d) Percentage error in the determination of g is 2.5%

(1990)

Column I

Column II

Capacitance

Ohm-second

Inductance

Coulomb2-joule–1

Magnetic induction

52. Match the physical quantities given in Column I with
dimensions expressed in terms of mass (M), length (L), time
(T ), and charge (Q) given in Column II and write the
correct answer against the matched quantity in a tabular
form in your answer book.
(1993)

47. In terms of potential difference V, electric current I,

permittivity ε 0 , permeability µ 0 and speed of light c, the
dimensionally correct equations is/are
(2015 Adv.)
(b) ε 0 I = µ 0V
(a) µ 0 I 2 = ε 0V 2
(c) I = ε 0 cV
(d) µ 0 cI = ε 0V

48. Planck’s 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 options is/are
(2015 Adv.)
(b) M ∝ G
(a) M ∝ c
(c) L ∝ h

(d) L ∝ G

Passage Based Questions

Column I

Column II

Angular momentum

[ ML2 T−2 ]

Latent heat


[ ML2 Q−2 ]

Torque

[ ML2 T−1 ]

Capacitance

[ ML3 T−1 Q−2 ]

Inductance

[ M −1 L−2 T2 Q2 ]

Resistivity

[ L2 T−2 ]

53. Some physical quantities are given in Column I and some

Passage
In electromagnetic theory, the electric and magnetic phenomena
are related to each other. Therefore, the dimensions of electric and
magnetic quantities must also be related to each other. In the
questions below, [E] and [ B ] stand for dimensions of electric and
magnetic fields respectively, while [ ε 0 ] and [µ 0 ] stand for
dimensions of the permittivity and permeability of free space,
respectively. [ L ] and [ T ] are dimensions of length and time,
respectively. All the quantities are given in SI units.
(There are two questions based on above).

(2018 Adv.)

49. The relation between [E] and [B] is
(a) [E] = [B] [L] [T]
(b) [E] = [B] [L]−1 [T]

(c) [E] = [B] [L] [T]−1
(d) [E] = [B] [L]−1 [T]−1

Coulomb (volt)–1, Newton
(ampere metre)–1,
volt-second (ampere)–1

possible SI units in which these quantities may be expressed
are given in Column II. Match the physical quantities in
Column I with the units in Column II.
(2007)
Column I

Column II

(p) (volt) (coulomb)
(A) GM e M s
(metre)
G — universal
gravitational constant,
M e — mass of the earth,
M s — mass of the sun.
(B)


3RT
(q) (kilogram) (metre) 3
M
(second) −2
R — universal gas constant,
T — absolute temperature,
M — molar mass.


General Physics 5
Column I

(C)

F

2

56. Two vectors A and B are defined as A = ai$

Column II
2

(r)

(metre) (second)

−2

q2B 2

F — force,
q — charge,
B — magnetic field.

and

B = a (cos ωt$i + sin ωt$j ), where a is a constant and
ω = π /6 rad s −1 . If | A + B | = 3 | A − B | at time t = τ for the
first time, the value of τ, in seconds, is ............. . (2018 Adv.)

Analytical & Descriptive Questions
57. Give the MKS units for each of the following quantities.

(farad) (volt)2

(s)
(D) GM e
Re
G — universal gravitational
constant,
M e — mass of the earth,
Re — radius of the earth.

(1980)

(kg)−1

(a) Young’s modulus
(b) Magnetic induction
(c) Power of a lens


58. A gas bubble, from an explosion under water, oscillates with

54. Match Column I with Column II and select the correct
answer using the codes given below the lists.
Column I

(2013 Main)

a period T proportional to p a d b E c , where p is the static
pressure, d is the density of water and E is the total energy of
the explosion. Find the values of a , b and c.
(1981)

59. Write the dimensions of the following in terms of mass,

Column II

time, length and charge.
(a) Magnetic flux
(b) Rigidity modulus

A.

Boltzmann’s constant

p.

[ ML2 T −1 ]


B.

Coefficient of viscosity

q.

[ ML−1 T −1 ]

C.

Planck’s constant

r.

[ MLT −3 K −1 ]

D.

Thermal conductivity

s.

[ ML2 T −2 K −1 ]

Integer Answer Type Questions

(1982)

60. N divisions on the main scale of a vernier calipers coincide
with ( N + 1) divisions on the vernier scale. If each division

on the main scale is of a units, determine the least count of
instrument.
(2003)

55. To find the distance d over which a signal can be seen

61. The edge of a cube is measured using a vernier caliper.

clearly in foggy conditions, a railway 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 S 1/ n . The value of n is

(9 divisions of the main scale is equal to 10 divisions of
vernier scale and 1 main scale division is 1 mm). The main
scale division reading is 10 and 1 division of vernier scale
was found to be coinciding with the main scale. The mass of
the cube is 2.736 g. Calculate the density in g/cm3 upto
correct significant figures.
(2005)

(2014 Adv.)

SECTION-2
Least count for length = 01
. cm, Least count for time = 01
. s

Objective Questions I (Only one correct option)

1. A student performs an experiment to determine the Young’s
modulus of a wire, exactly 2 m long, by Searle’s method. In a
particular reading, the student measures the extension in the
length of the wire to be 0.8 mm with an uncertainty of
±0.05 mm at a load of exactly 1.0 kg. The student also
measures the diameter of the wire to be 0.4 mm with an
uncertainty of ±0.01 mm. Take g = 9.8 m /s 2 (exact). The
Young’s modulus obtained from the reading is close to
(2007)

Length of
Number of
the
oscillations
Student
pendulum
(n)
(cm)

I
II
III

64.0
64.0
20.0

8
4
4


Total time
for (n)
oscillations
(s)

128.0
64.0
36.0

Time
period
(s)

16.0
16.0
9.0

If EI , EII and EIII are the percentage errors in g, i.e.

 ∆g
× 100 for students I, II and III, respectively


 g
(2008)

(b) ( 2.0 ± 0.2 ) × 1011 N/ m2
(a) ( 2.0 ± 0.3 ) 1011 N/ m2
(c) (2.0 ± 0.1) × 1011 N/ m2 (d) ( 2.0 ± 0.05 ) × 1011 N/ m2


(a) EI = 0 (b) EI is minimum (c) EI = EII (d) EII is maximum

2. Students I, II and III perform an experiment for measuring

3. The density of a solid ball is to be determined in an

the acceleration due to gravity (g) using a simple pendulum.
They use different lengths of the pendulum and/or record
time for different number of oscillations. The observations
are shown in the table.

experiment. The diameter of the ball is measured with a
screw gauge, whose pitch is 0.5 mm and there are
50 divisions on the circular scale. The reading on the main
scale is 2.5 mm and that on the circular scale is 20 divisions.


6 General Physics
If the measured mass of the ball has a relative error of 2%,
the relative percentage error in the density is
(2011)
(a) 0.9%
(b) 2.4%
(c) 3.1%
(d) 4.2%

Y
P


4. The diameter of a cylinder is measured using a vernier
calipers with no zero error. It is found that the zero of the
vernier scale lies between 5.10 cm and 5.15 cm of the main
scale. The vernier scale has 50 division equivalent to
2.45 cm. The 24th division of the vernier scale exactly
coincides with one of the main scale divisions. The diameter
of the cylinder is
(2013 Adv.)
(a) 5.112 cm (b) 5.124 cm (c) 5.136 cm (d) 5.148 cm

5. The current voltage relation of diode is given by
I = ( e1000 V / T − 1) mA, where the applied voltage V is in volt
and the temperature T is in kelvin. If a student makes an
error measuring ± 0.01 V while measuring the current of
5 mA at 300 K, what will be the error in the value of current
in mA?
(2014 Main)
(a) 0.2 mA
(b) 0.02 mA
(c) 0.5 mA
(d) 0.05 mA

6. There are two vernier calipers both of which have 1 cm
divided into 10 equal divisions on the main scale. The
vernier scale of one of the calipers (C1 ) has 10 equal
divisions that correspond to 9 main scale divisions. The
vernier scale of the other caliper (C 2 ) has 10 equal divisions
that correspond to 11 main scale divisions. The readings of
the two calipers are shown in the figure. The measured
values (in cm) by calipers C1 and C 2 respectively, are

(2016 Adv.)

2

3

4

C1
5

0
2

3

10
4

C2
5

(b) 2.87 and 2.83
(d) 2.87 and 2.86

whose total mass remains constant. The expansion is such
that the instantaneous density ρ remains uniform throughout
 1 dρ 
the volume. The rate of fractional change in density 
 is

 ρ dt 
constant. The velocity v of any point of the surface of the
expanding sphere is proportional to
(2017 Adv.)
(b)

1
R

S

O

Q

R=Q–P
Q

X

(a) S = (1 − b 2 ) P + bQ
(b) S = ( b − 1) P + bQ
(c) S = (1 − b ) P + bQ
(d) S = (1 − b ) P + b 2Q

Objective Questions II (One or more correct option)
9. Consider a vernier caliper in which each 1 cm on the main
scale is divided into 8 equal divisions and a screw gauge
with 100 divisions on its circular scale. In the vernier
callipers, 5 divisions of the vernier scale coincide with 4

divisions on the main scale and in the screw gauge, one
complete rotation of the circular scale moves it by two
divisions on the linear scale. Then
(2015 Adv.)
(a) if the pitch of the screw gauge is twice the least count of
the vernier caliper, the least count of the screw gauge is
0.01 mm
(b) if the pitch of the screw gauge is twice the least count of
the Vernier caliper, the least count of the screw gauge is
0.005 mm
(c) if the least count of the linear scale of the screw gauge is
twice the least count of the Vernier calipers, the least
count of the screw gauge is 0.01 mm
(d) if the least count of the linear scale of the screw gauge is
twice the least count of the vernier caliper, the least
count of the screw gauge is 0.005 mm.
the formula used for the time period of a periodic motion is
7( R − r )
. The values of R and r are measured to be
T = 2π
5g

10

7. Consider an expanding sphere of instantaneous radius R

(a) R

S


10. In an experiment to determine the acceleration due to gravity g,
0

(a) 2.87 and 2.87
(c) 2.85 and 2.82

P

bR

2

(c) R 3

(d) R 3

8. Three vectors P, Q and R are shown in the figure. Let S be
any point on the vector R. The distance between the points P
and S is b | R |. The general relation among vectors P, Q and
(2017 Adv.)
S is

( 60 ± 1) mm and (10 ± 1) mm, respectively. In five successive
measurements, the time period is found to be 0.52 s, 0.56 s,
0.57 s, 0.54 s and 0.59 s. The least count of the watch used for
the measurement of time period is 0.01 s. Which of the
following statement(s) is (are) true?
(2016 Adv.)
(a) The error in the measurement of r is 10%
(b) The error in the measurement of T is 3.57%

(c) The error in the measurement of T is 2%
(d) The error in the measurement of g is 11%

11. A length-scale (l) depends on the permittivity ( ε ) of a
dielectric material, Boltzmann’s constant ( kB ), the absolute
temperature (T ), the number per unit volume ( n ) of certain
charged particles, and the charge ( q ) carried by each of the
particles. Which of the following expression (s) for l is (are)
dimensionally correct?
(2016 Adv.)


General Physics 7
 nq 2 
(a) l = 

 ε kB T 

 εk T 
(b) l =  B2 
 nq 


q2 
(c) l =  2 / 3

 ε n kB T 


q2 

(d) l =  1 / 3

 ε n kB T 

If the measurement errors in all the independent quantities are
known, then it is possible to determine the error in any dependent
quantity. This is done by the use of series expansion and truncating
the expansion at the first power of the error. For example, consider
the relation z = x / y. If the errors in x, y and z are ∆x, ∆y and ∆z
respectively, then
x ± ∆x x  ∆x   ∆y 
= 1 ±  1 ± 
y ± ∆y y 
x 
y

 ∆y
The series expansion for 1 ± 

y

(2011)

14. Taking the electronic charge as e and the permittivity as ε 0 ,

Passage Based Questions
Passage 1

z ± ∆z =


To sustain the oscillations, a time varying electric field needs to be
applied that has an angular frequency ω, where a part of the energy
is absorbed and a part of it is reflected. As ω approaches ω p , all the
free electrons are set to resonance together and all the energy is
reflected. This is the explanation of high reflectivity of metals.

−1

−1

to first power in ∆y / y, is

1m ( ∆y / y ). The relative errors in independent variables are always
added. So, the error in z will be
 ∆x ∆y 
+ 
∆z = z 
 x
y

use dimensional analysis to determine the correct expression
for ω p .
(a)

Ne
mε 0

(b)

(c)


Ne2
m ε0

(d)

m ε0
Ne
m ε0
Ne2

15. Estimate the wavelength at which plasma reflection will
occur for a metal having the density of electrons
N ≈ 4 × 1027 m −3 . Take ε 0 ≈ 10−11 and m ≈ 10−30 , where
these quantities are in proper SI units.
(a) 800 nm
(b) 600 nm
(c) 300 nm
(d) 200 nm

Passage 3

13. In an experiment, the initial number of radioactive nuclei is

16. The phase space diagram for a ball thrown vertically up

3000. It is found that 1000 ± 40 nuclei decayed in the first
1.0 s. For | x|<< 1, ln (1 + x ) = x up to first power in x. The
error ∆λ, in the determination of the decay constant λ ins −1 , is
(a) 0.04

(b) 0.03
(c) 0.02
(d) 0.01

Momentum

The above derivation makes the assumption that ∆x / x << 1,
∆ y / y << 1. Therefore, the higher powers of these quantities are
neglected.
(There are two questions based on above paragraph). (2018 Adv.)
(1 − a )
to be determined by
12. Consider the ratio r =
(1 + a )
measuring a dimensionless quantity a. If the error in the
measurement of a is ∆ a ( ∆ a / a << 1), then what is the error
∆r in determining r ?
∆a
− 2∆a
(b)
(a)
2
(1 + a )
(1 + a )2
2∆a
2a∆a
(c)
(d)
(1 − a )2
(1 − a 2 )


Phase space diagrams are useful tools in
analysing all kinds of dynamical
problems. They are especially useful in
studying the motion where position and
momentum are changed. Here we
consider some simple dynamical systems
in one-dimension. For such systems,
phase space is a plane in which position
Position
is plotted along horizontal axis and
momentum is plotted along vertical axis.
The phase space diagram is x( t ) vs p ( t ) curve in this plane. The
arrow on the curve indicates the time flow. For example, the phase
space diagram for a particle moving with constant velocity is a
straight line as shown in the figure. We use the sign convention in
which position or momentum upwards (or to right) is positive and
downwards (or to left) is negative.
(2011)
from ground is
Momentum

(a)

Position

Passage 2
A dense collection of equal number of electrons and positive ions
is called neutral plasma. Certain solids containing fixed positive
ions surrounded by free electrons can be treated as neutral plasma.

Let N be the number density of free electrons, each of mass m.
When the electrons are subjected to an electric field, they are
displaced relatively away from the heavy positive ions. If the
electric field becomes zero, the electrons begin to oscillate about
the positive ions with a natural angular frequency ω p , which is
called the plasma frequency.

Momentum

(b)

Position

Momentum

(c)

Momentum

(d)

Position

Position


8 General Physics
17. The phase space diagram for simple harmonic motion is a
circle centered at the origin. In the figure, the two circles
represent the same oscillator but for different initial

conditions, and E1 and E2 are the total mechanical energies
respectively. Then,
Momentum

E1

E2

1.0 × 10−5 m. The maximum percentage error in the
Young’s modulus of the wire is
(2014 Adv.)

2a

(a) E1 = 2 E2
(c) E1 = 4 E2

20. The energy of a system as a function of time t is given as

Position

a

The 20th division of the vernier scale exactly coincides with
one of the main scale divisions. When an additional load of
2 kg is applied to the wire, the zero of the vernier scale still
lies between 3.20 × 10−2 m and 3.25 × 10−2 m of the main
scale but now the 45th division of vernier scale coincides
with one of the main scale divisions. The length of the thin
metallic wire is 2 m and its cross-sectional area is

8 × 10−7 m2 . The least count of the vernier scale is

E ( t ) = A 2 exp ( −αt ), where α = 0.2 s −1 . The measurement
of A has an error of 1.25%. If the error in the measurement of
time is 1.50%, the percentage error in the value of E ( t ) at
t = 5 s is

(b) E1 = 2 E2
(d) E1 = 16 E2

(2015 Adv.)

21. A steel wire of diameter 0.5 mm and Young’s modulus

18. Consider the spring-mass system, with the mass submerged
in water, as shown in the figure. The phase space diagram for
one cycle of this system is

2 × 1011 Nm−2 carries a load of mass m. The length of the
wire with the load is 1.0 m. A vernier scale with 10 divisions
is attached to the end of this wire. Next to the steel wire is a
reference wire to which a main scale, of least count 1.0 mm,
is attached. The 10 divisions of the vernier scale correspond
to 9 divisions of the main scale. Initially, the zero of vernier
scale coincides with the zero of main scale. If the load on the
steel wire is increased by 1.2 kg, the vernier scale division
which coincides with a main scale division is ......... .
(2018 Adv.)
(Take, g = 10 ms −2 and π = 3. 2).


Analytical & Descriptive Questions
Momentum

Momentum

(a)

(b)
Position

Position

Momentum

(c)

Momentum

(d)
Position

22. The pitch of a screw gauge is 1 mm and there are
100 divisions on the circular scale. While measuring the
diameter of a wire, the linear scale reads 1 mm and 47th
division on the circular scale coincides with the reference
line. The length of the wire is 5.6 cm. Find the curved surface
area (in cm 2 )of the wire in appropriate number of significant
figures.

(2004)


23. In a Searle’s experiment, the diameter of the wire as
Position

Integer Answer Type Questions
19. During Searle’s experiment, zero of the vernier scale lies
between 3.20 × 10−2 m and 3.25 × 10−2 m of the main scale.

measured by a screw gauge of least count 0.001 cm is
0.050 cm. The length, measured by a scale of least count
0.1 cm, is 110.0 cm. When a weight of 50 N is suspended
from the wire, the extension is measured to be 0.125 cm by a
micrometer of least count 0.001 cm. Find the maximum error
in the measurement of Young’s modulus of the material of
the wire from these data.
(2004)


SECTION-3
Match the Columns
1. Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system.
Match the statements in Column I to the appropriate process (es) from Column II.

(2009)

Column I

Column II

(A) The energy of the system is increased.


(p)

System : A capacitor, initially uncharged.
Process : It is connected to a battery.
System : A gas in an adiabatic container fitted with an adiabatic
piston.
Process : The gas is compressed by pushing the piston.
System : A gas in a rigid container.
Process : The gas gets cooled due to colder atmosphere
surrounding it.
System : A heavy nucleus, initially at rest.
Process : The nucleus fissions into two fragments of nearly
equal masses and some neutrons are emitted.
System : A resistive wire loop.
Process : The loop is placed in a time varying magnetic field
perpendicular to its plane.

(B) Mechanical energy is provided to the system, which is (q)
converted into energy of random motion of its parts.
(C) Internal energy of the system is converted into its (r)
mechanical energy.
(D) Mass of the system is decreased.

(s)
(t)

2. Column II shows five systems in which two objects are labelled as X and Y . Also in each case a point P is shown. Column I gives
some statements about X and/or Y . Match these statements to the appropriate system(s) from Column II
Column I


(A)

(2009)

Column II

The force exerted by X
on Y has a magnitude Mg.

Y

(p)

Block Y of mass M left on a fixed
inclined plane X , slides on it with a
constant velocity.

(q)

Two ring magnets Y and Z, each of
mass M , are kept in frictionless vertical
plastic stand so that they repel each
other. Y rests on the base X and Z hangs
in air in equilibrium. P is the topmost
point of the stand on the common axis
of the two rings. The whole system is in
a lift that is going up with a constant
velocity.
A pulley Y of mass m0 is fixed to a table

through a clamp X . A block of mass M
hangs from a string that goes over the
pulley and is fixed at point P of the
table. The whole system is kept in a lift
that is going down with a constant
velocity.
A sphere Y of mass M is put in a
non-viscous liquid X kept in a container
at rest. The sphere is released and it
moves down in the liquid.

X
P

(B)

The gravitational potential energy of
X is continuously increasing.

P
Z
Y
X

(C)

Mechanical energy of the system
X + Y is continuously decreasing.

Y

P

(r)

X

(D)

The torque of the weight of Y about
point P is zero.

(s)
Y
P

X

(t)

A sphere Y of mass M is falling with its
terminal velocity in a viscous liquid X
kept in a container.


Answers
Section 1
−1

2


−3

−2

4

57. (a) N/m 2
5
58. a = − , b =
6

4

1. [ML T ]

2. [M L T Q ]

3. [M −1 L −3 T 3 A 2 ]

4. [ML 5 T −2 ]

5. (b)

6. (*)

7. (d)

8. (a)

9. (d)

13. (d)
17. (a)

10. (a)
14. (c)
18. (b)

11. (d)
15. (b)
19. (a)

12. (a)
16. (b)
20. (d)

21. (c)

22. (a)

23. (c)

24. (c)

1. (b)

25. (d)

26. (c)

27. (d)


28. (c)

5. (a)

29. (a)

30. (a)

31. (c)

32. (*)

9. (b,c)

33. (b)

34. (b)

35. (b)

36. (d)

37. (c)

38. (b)

39. (b)

40. (b)


41. (a,c)

42. (a,d)

43. (a,b,c)

44. (b,c)

45. (a,b,c,d) 46. (a,c)

47. (a,c)

48. (a,c,d)

49. (c)

51. (See the solution)

50. (d)

59. (a) [ML 2T −1Q −1] (b) [ML −1T −2]
a
60.
61. 2.66 g/cm 3
N +1

Section 2
2. (b)


3. (c)

6. (b)

4. (b)

7. (a)

8. (c)

10. (a,b,d)

11. (b,d)

12. (b)

13. (c)

14. (c)

15. (b)

16. (b)

17. (c)

18. (b)

21. (3)


19. (4)

22. 2.6 cm

20. (± 4%)

23. 109
. × 10 N/m 2

2

10

Section 3

52. (See the solution)

53. A-p,q B-r,s C-r,s D-r,s

1. A-p,q,s,t

54. A-s B-q C-p D-r

55. (3)

2. A-p,t

56. (2)

(c) m −1


(b) Tesla
1
1
,c=
2
3

B-q

B-q,s,t

C-s

D-s

C-p.r.s,t

D-q

Hints & Solutions
Section-1
E = hν

1.
∴

E
ν


h=

or [ h ] =

[ E ] [ML2 T−2 ]
=
= [ML2 T−1 ]
[ ν]
[T−1 ]

[ X ] = [C ] = [ M –1 L–2 T2 Q2 ]

2.

[ Z ] = [ B ] = [M T Q ]
–1

∴

[Y ] =

[M −1 L−2 T2 Q2 ]
[MT−1 Q−1 ]2

–1

[σ ] =

X 


Q Given Y = 2 

3Z 

= [M −3 L−2 T4 Q4 ]

3. Electrical conductivity, σ =
=

qi
( it )( i ) i 2 t
=
=
FA
FA
FA
[A 2 ] [T]
[MLT−2 ][L2 ]

∴

5.

●

NOTE From this question, students can take a lesson that in
IIT-JEE also questions may be wrong or there may be no correct
answer in the given choices. So, don't waste time if you are
confident.


7. C =

∆q
A ∆q
( ∆q ) L
or ε 0
or ε 0 =
=
∆V
L ∆V
A.( ∆V )

J
i/ A
=
E F/q

= [M −1 L−3 T3 A 2 ]

a

4.  2  = [ p ]
V 

1
ε 0 E 2 is the expression of
2
energy density (Energy per unit volume)
 ML2 T−2 
1

2
−1 −2
ε
E
=
0
 2
  L3  = [ ML T ]



6. (None of the four choices)

[ a ] = [ pV 2 ] = [ML−1 T−2 ] [L6 ] = [ ML5 T−2 ]


Capacitance
X  
[Y ] =  2  = 
2
 Z   ( Magnetic induction ) 
 M −1 L−2 Q2 T2 
=  2 −2 −2  = [M −3 L−2 T4 Q4 ]
 M Q T 

X = ε0 L
but

∆V
( ∆q )L

∆V
L
=
∆t
A ( ∆V ) ∆t

[ A ] = [ L2 ]
X =

∴

∆q
= current
∆t

8. V = l 3 = (1.2 × 10−2 m )3 = 1.728 × 10−6 m3
Q Length ( l ) has two significant figures, the volume (V )
should also have two significant figures. Therefore, the
`correct answer is
V = 1.7 × 10−6 m3

9. Density, ρ =

m

π r2 L
∆ρ
∆r ∆L
 ∆m
∴

× 100 = 
+2
+
 × 100
 m
r
L
ρ


General Physics 11
or maximum percentage error in density
2 × 0.005
0.06

 0.003
=
× 100 +
× 100 +
× 100
0.5
6

 0.3
= 4%
αZ 
0 0 0
 k θ = [M L T ]
 
 kθ 

[α ] =  
Z

10.

Further
∴

16. If student measures 3.50 cm, it means that there is an
uncertainly of order 0.01 cm.
1
1 MSD =
cm and 9 MSD = 10 VSD
10
LC of vernier caliper = 1MSD − 1VSD
9
1
1
cm = 0.01 cm
= 1 −  =
10 100
10 

α 
[ p] =  
β 
 α   kθ 
[β ] =   =  
 p   Zp 


Dimensions of k θ are that to energy as E =

3
kT . Hence,
2

 ML2 T−2 
[β ] = 
= [ M 0 L2 T0 ]
−1 −2 
LML
T



11. Dipole moment = (charge) × (distance)
Electric flux = (electric field) × (area)
Hence, the correct option is (d).
Pitch
12. Least count (LC) =
Number of divisions on circular scale
0.5
= 0.01mm
=
50
Positive zero error = 5 × 0.01 mm = 0.05 mm
NOTE

Positive zero error is finally substracted.


Now, diameter of ball
= ( 2 × 0.5 mm ) + 25 × 0.01 mm − 0.05 mm = 1.2 mm

13. Least count of vernier calipers
or

LC = 1MSD – 1 VSD
Smallest division on main scale
Number of divisions on vernier scale

20 divisions of vernier scale = 16 divisions of main scale
16
16
MSD =
mm = 0.8 mm
∴ 1 VSD =
20
20
LC = 1MSD – 1VSD = 1 mm − 0.8 mm = 0.2 mm
∴
∴ Correct option is (d).
0.5
14. ∆d = ∆l =
mm = 0.005 mm
100
4 MLg
Y =
πld 2
 ∆d 
 ∆l 

 ∆Y 
⇒
=   + 2 


 d 
 Y  max  l 
∆d (0.5 / 100)
 ∆l  0.5 / 100
= 0.02 and
=
= 0.01
  =
 l
0.25
0.5
d
or

∆l
∆d
= 2⋅
l
d

1 q1 q2
qq
, ε0 = 1 2 2
4 πε 0 R 2
4 πFR

Substituting the units, we have
[AT]2
C2
[
]
ε0 =
⇒
ε
=
= [M −1 L−3 T4 A 2 ]
0
[MLT−2 ] [L2 ]
N-m2

15. From Coulomb’s law, F =

17. Time period is given by, T =
T = 2π

Further,
⇒

g=

( 4 π 2 )L
T

2

=


t
n

L
g

( 4 π 2 )( L )
t
 
 n

2

= ( 4π 2n2 )

L
t

2

or

g∝

L
t2

Percentage error in the value of ‘g’ will be
∆g

 ∆t 
 ∆L
× 100 =   × 100 + 2   × 100
 t 
 L
g
=

.
01
 1
× 100 + 2 ×   × 100 = 2.72%
 90
20

∴ The nearest answer is 3%

18. Least count
pitch
0.5 mm
=
number of divisions on circular scale
50
∴ LC = 0.01mm
Negative zero error = ( 50 − 45 ) LC = 0.05 mm
=

Measured value = main scale reading + screw gauge reading
+ Negative zero error
= 0.5 mm + {25 × 0.01 + 0.05} mm = 0.8 mm


19. T = t1 + t 2

or T =
T=

2L
L
+ , g = 10 m/s 2
g
Vs
L
L
+
5 300

Differentiating equations, we get
1 1 −1 / 2

 1
dT =
L dL + 
dL
 300 
52
1 1
dL
dL +
= 0.01
300

2 5 20
1 
 1
dL  +
 = 0.01
 20 300

dT or δT =

3
 16 
= 0. 01, dL =
dL

300
16




12 General Physics
3
dL
× 100 =
×
16
L
∆m
20. Given,
× 100 = 1.5%

m
m
∆d
× 100 =
d= 3 ⇒
d
l

15 ~
1
× 100 =
− 1%
16
20
∆l
and
× 100 = 1%
l
∆m
3∆l
× 100 +
× 100
m
l

Now, using given relation,
X = 5YZ 2
[X ]
[Y ] = 2
[Z ]

 M−1L−2A 2T 4  M−1L−2A 2T 4
=  1 0 −2 −1 2  =
M2T −4A −2
(M L T A ) 

= 1.5 + 3 = 4.5%
Pitch
LC =
number of division
0.5
mm
LC =
100
LC = 5 × 10−3 mm

21.

∴

24. Let

…(i)
−3

t = 5.5 mm + ( 48 + 3 ) × 5 × 10 mm

⇒

t = 5.755 mm
[ R ] = [ ε 0 ]α [µ 0 ]β

[R ] = [M L T
1

2

−3

…(i)
−2

A ] , [ ε0 ] = [ M

−1

−3

L

4

[ I] = [mass × distance 2 ]

2

T A ],

= [ ML2T 0 ]
[ S] = [force × length] = [ ML0T −2 ]
[ h] = [ML2T −1 ]


[ M1 L2 T −3 A −2 ] = [ M−1 L−3 T 4A 2 ]α [ M1 L1 T −2 A −2 ]β
−3

−2

−α + β

−3 α + β

4α − 2β

[M L T A ] = [ M
L
T
Comparing both sides, we get
−α +β =1
−3 α + β = 2
4 α − 2 β = −3
2 α − 2 β = −2
Solving above equations, we get
−1
1
and β = +
α=
2
2
 µ 
∴
[ R ] = [ ε 0 ]−1 / 2 [µ 0 ]1 / 2 =  0 
 ε0 

1
23. U = CV 2
2
U 
∴
[C ] =  2 
V 
As, V = potential =

potential energy
charge

We have,
[U ]
[ q 2 ]  A 2T 2 
=
=

U 2  [U ]  ML2T −2 
 2
q 
X = [M−1L−2A 2T 4 ]

[C ] =

∴
Further,

F = BIl ⇒ [ B ] =
∴


…(i)

Then, the respective dimensions of the given physical
quantities, i.e.
[ p ] = [mass × velocity] = [ MLT −1 ]

Now, from Eq. (i), we get
2

[ p ] = [ h ]a [ S]b [ I]c

Thus,

[µ 0 ] = [ M1 L1 T −2 A −2 ]

1

p ∝ ( h )a ( S )b ( I )c

or
p = kh a S b I c
where, k is a dimensionless proportionality constant.

Now,

22. Let

[Y ] = [M−3L−2A 4T 8 ]


[F]  MLT −2 
=

[I][l]  AL 

Z = [M1L0T −2A −1 ]

A

2α − 2β

Then, substituting these dimensions in Eq. (i), we get
[MLT −1 ] = [ML2T −1 ]a [MT −2 ]b [ML+2 ]c

]

…(ii)
…(iii)
…(iv)
…(v)

For dimensional balance, the dimensions on both sides
should be same.
Thus, equating dimensions, we have
a+ b+ c=1
1
2( a + c ) = 1 or a + c =
2
− a − 2b = − 1 or a + 2b = 1
Solving these three equations, we get

1
1
a = 0, b = , c =
2
2
1 1

1 1

∴

p = h 0 S 2 I 2 or

p = S 2 I 2 h0

25. Dimensions of ε 0 (permittivity of free space) are
[ ε 0 ] = [ M−1L−3T 4A 2 ]
As,
c = speed of light.
∴ Dimension of [ c] = [LT −1 ]
So, dimensions of

ε0
are
µ0

 ε 0   ε 20 
 2
1 
 = [ ε 0 c] Q c =

=

µ 0 ε 0 

 µ 0   ε 0µ 0 
= [M−1L−3T 4A 2 ][LT −1 ] = [M−1L−2T3 A 2 ]

26. Dimensions of given quantities are
l = inductance = [ M1 L2 T −2 A −2 ]
r = resistance = [ M1 L2 T −3 A −2 ]
c = capacitance = [ M− 1 L− 2 T 4 A 2 ]
v = voltage = [ M1 L2 T −3 A −1 ]


General Physics 13
l
are
rcv
[ ML2 T −2 A −2 ]

⇒

So, dimensions of

 l 
−1
 rcv = [ M1 L2 T −2 A −1 ] = [ A ]

Here k is a dimensionless constant.
For calculating the values of a , b and c, compare the

dimensional formula for both side.
LHS t = time = [ M0 L0 T1 ]

Dimensions of acceleration are, [ A ] = [LT −2 ]
Dimensions of force are, [ F] = [ MLT −2 ]
Dimension of Young modulus is, [Y] = [ ML−1T −2 ]

RHS G =

Let dimensions of Young’s modulus is expressed in terms
of speed, acceleration and force as;
β

γ

…(i)
[ Y] = [ V] [ A ] [ F]
Then substituting dimensions in terms of M, L and T we get,
[ML−1T −2] = [LT −1 ]α [LT −2 ]β [ MLT −2 ]γ
= [ Mγ Lα +β + γ T − α − 2β − 2γ ]
Now comparing the powers, we get
γ =1
α + β + γ = −1
and
−α − 2β − 2γ = −2
Solving these we get;
α = −4, β = 2, γ = 1
Substituting α ,β , & γ in (i) we get;
[Y] = [ V −4 A 2F ]


28. Force of interaction between two atoms is given as
F = αβ exp ( − x2 / αkT )
As we know, exponential terms are always dimensionless, so
 − x2 
dimensions of 
 = [ M0 L0 T 0 ]
kT
α


⇒ Dimensions of α = Dimension of ( x2 / kT )
Now, substituting the dimensions of individual term in the
given equation, we get
[M0 L2 T 0 ]
= 1 2 − 2 {Q Dimensions of kT equivalent to the
[M L T ]
dimensions of energy = [ M1 L2 T − 2 ] }
= [ M− 1 L0 T 2 ]
Now, from given equation, we have dimensions of
F = dimensions of α × dimensions of β
F
⇒ Dimensions of β = Dimensions of  
α
=

[M1 L1 T − 2 ]

128 × 1000 × 25 × 25 × 25
= 40
50 × 100 × 100 × 100


30. Let t = k (G )a ( h )b ( c )c

27. Dimensions of speed are, [ V] = [LT −1 ]

α

N2 =

= [ M2 L1 T − 4 ]
[M−1 L0 T 2 ]

…(i)

[Qusing Eq. (i)]

29. To convert a measured value from one system to another
system, we use, N 1 u1 = N 2 u2
where, N is numeric value and u is unit.
We get
kg
50 g
mass 

128 ⋅ 3 = N 2
Qdensity =
3 

volume
m

( 25 cm) 
128 × 1000 g
N 2 × 50 g
⇒
=
100 × 100 × 100 cm3 25 × 25 × 25 cm3

F ⋅ r2 kg ms–2 × m 2
=
= [ M−1 L3 T −2 ]a
m1 m2
( kg )2

h = [ M1 L2 T −1 ] b
d
c = = [ M0 L1 T −1 ]c
t
Compare both side for powers of M, L and T,
M⇒0 = − a + b
L ⇒ 0 = 3a + 2b + c
T ⇒1 = − 2a − b − c
Solving Eqs. (i), (ii), (iii), we get
1
1
−5
a = , b = and c =
2
2
2
So, put these values in Eq. (i)

Gh
t = k G1 / 2 h1 / 2 c−5 / 2 ⇒ t = k 5
c
Gh
So,
t∝
c5

…(i)
…(ii)
…(iii)

31. Area of one square = 5.29 cm 2
Area of seven such squares
= 7 times addition of area of one square
= 5.29 + 5.29 + 5.29 K 7 times
= 37.03 cm 2
As we know that, if in the measured values to be
added/subtracted the least number of significant digits after
the decimal is n.
Then, in the sum or difference also, the number of significant
digits after the decimal should be n.
Here, number of digits after decimal in 5.29 is 2, so our
answer should also contain only two digits after decimal
point.
∴ Area required = 37.03 cm 2

32. Given, mass = (10.00 ± 010
. ) kg
Edge length = ( 010

. ± 0.01) m
Error in mass,
.
∆M 01
=
10
M
and error in length,
∆l 0.01
=
01
.
l
Density of the cube is given by
ρ=

Mass
M
=
Volume l 3

…(i)

…(ii)


14 General Physics
∴ Permissible error in density is

or


∆ρ ∆M
∆l
…(iii)
=
±3
M
l
ρ
Substituting the value from Eqs. (i) and (ii) in Eq. (iii), we get

⇒
Since,

⇒ g=

cosθ = −

= 6 | A1 |2 − 6 | A 2 |2 + 5 A1 ⋅ A 2
= 6 | A1 |2 − 6 | A 2 |2 + 5| A1 || A 2 |cos θ

= − 118.5

37.
…(i)

Given, ∆l = 01
. cm, l = 55 cm, ∆T = 1s and T for
20 oscillations = 30 s
Substituting above values in Eq. (i), we get

.
1
∆g 01
=
+ 2×
30
g
55
Hence, percentage error in g is
10 20
∆g
=
× 100 =
+
= 6.8%
55 3
g

34. Volume of a cylinder of radius ‘r’ and height h is given by
1
πD 2 h,
4
where D is the diameter of circular surface.
Here, D = 12.6 cm and h = 34.2 cm
π
⇒
V = × (12.6 )2 × ( 34.2 )
4
V = 4262.22 cm3
V = 4260 (in three significant numbers)

Now, error calculation can be done as
∆V
.
0.1
 ∆D  ∆h 2 × 01
= 2
=
+
 +
 D
V
h
12.6
34.2
~ 80 cm3
⇒
∆V = 79.7 −
V = πr2 h or V =

V = 4260 ± 80 cm3

Hence,

35. In a screw gauge,
Least count
=

Measure of 1 main scale division (MSD)
Number of division on circular scale


Here, minimum value to be measured/least count is 5 µm.
= 5 × 10−6 m
∴ According to the given values,
5 × 10−6 =

1 × 10−3
N

 −3
= 6 × 9 − 6 × 25 + 5 × 3 × 5 ×  
 10 

4π 2l

T2
So, fractional error in value of g is
∆g ∆l 2∆T
=
+
g
l
T

1000
5

3
10
Now, ( 2 A1 + 3 A 2 ) ⋅ ( 3 A1 − 2 A 2 )


∴

But there is no option with unitless error. Hence, no option is
correct.
l
g

5 × 10

=

5 = ( 3 )2 + ( 5 )2 + 2 × 3 × 5cosθ

∆ρ
should be unitless quantity.
ρ

33. T = 2π

−6

= 200 divisions

36.

1
3
31
.
0.01

∆ρ 01
=
+
=
=
+ 3×
100 10 100
01
.
10
ρ
31
∆ρ
=
= 0.31
100
ρ

10−3

N =

A 2 + B 2 + 2 AB cosθ = n A 2 + B 2 − 2 AB cosθ
and

B=A

Solving, we get

 n 2 − 1

θ = cos −1  2

 n + 1

38. In the given cube, coordinates of point G (centre point of
a
a
, y1 = 0, z1 =
2
2
and coordinates of point H (centre point of BEFO) are
a
a
x2 = 0, y2 = , z 2 =
2
2
So, vector GH is
$
GH = ( x2 − x1 )$i + ( y2 − y1 )$j + ( z 2 − z1 )k
ABOD) are x1 =

=−

a $ a$ a $ $
i + j = ( j − i)
2
2
2

39. In first case :

R 2 = ( 2F )2 + ( 3F )2 + 2( 2F ) ( 3F ) cosθ
or

R 2 = 13F 2 + 12F 2 cos θ

...(i)

In second case :
( 2R )2 = ( 2F )2 + ( 6F )2 + 2 × 2 × 6 F 2 cos θ
⇒

4 R 2 = 40F 2 + 24 F 2 cos θ

… (ii)

Solving these two equations, we get
θ = 120º

40. Thickness = M.S Reading + Circular Scale Reading (L.C.)
0.1
= 0.002 cm per division
50
So, 2.124 cm is the correct answer.
L
41. CR and both are time constants. Their unit is second.
R
1
R
and have the SI unit (second )−1 . Further,
∴

CR
L
1
resonance frequency, ω =
LC
Here, L.C =