Course File
Dr. Anuj Kumar Agarwal
2020 -21 (odd)
UNIT I
Vector: - Scalar and vector quantities: Addition, Subtraction; Cartesian components of vector, Scalar and vector product of two vectors.
Force and Motion: Parabolic motion, projectiles thrown horizontally and at an angle. Ordinary problems on time of flight, horizontal range, and vertical height. Gravitational force, Kepler's laws; Elementary concept of Escape velocity and geostationary satellite.
1. Distinguish between scalar and vector quantities with suitable examples.
2. List separately scalar and vector quantities from the following – time, force, work, torque, velocity, acceleration, temperature, speed, energy, distance.
3. Define the following – (i) Null vector (ii) unit vector (iii) equal vector (iv) negative (v) co –initial vector (vi) co – linear vector.
4. Define scalar and vector products of two vectors. If A=2i+5j+3k, B=3i+5j-3k. Find the value of (i) (A × B) & (ii) A.B.
5. Find the angle between the vectors A = i+j-2k and B = -i+2j-k. [VJ Pg. 3.9] 6. Prove that vectors A = i+2j+3k and B = 2i-j are perpendicular to each other. [V.J. Pg. 3.9]
7. If magnitudes of two vectors A and B are 3 & 4 respectively and the dot product is 6 then find the angle between them.
8. Determine the value of ‘m’ so that the vectors A = 4i+mj-2k and B =2i+3j+k are perpendicular. [VJ Pg. 3.10]
9. If A.B = -AB. What is the angle between A & B.
10. A particle is acted upon by a constant force 4i+j-3k and 3i+j-k and is displaced from the point (1, 2, 3) to the point (5, 4, 1). Find the total work done. [VJ Pg. 3.10]
11. What do you understand by projectile motion? Prove that the trajectory of projectile is a parabola. 12. A body is projected in a direction making an angle θ to the horizontal. Write the expression for
(i) the time of flight, (ii) maximum height and (iii) horizontal range of a particle
13. A body is projected in a direction making an angle θ to the horizontal. Find the time of flight, Maximum height and horizontal range of the projectile in the following two cases
(a) Velocity = 20m/s, angle θ = 45 (b) Velocity=36m/s, angle θ = 30 [VJ Pg. 10.27, Unsol.Ques.] ⁰ ⁰
14. The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/sec can go without hitting the ceiling of the hall? [VJ Pg. 10.26, Ex-17]
15. (i) What do you mean by Newton’s law of gravitational force?
(ii) The body of mass 100 kg is placed 2 m away from another body of mass 50 kg. Find the gravitational attraction force acting between them. (G = 6.67×10-11 Nm2/kg2) [PSK Pg. 88, Ex-35]
16. Define gravitational acceleration ‘g’ and universal gravitational constant ‘G’. 17. Derive relation between ‘g’ and ‘G’.
18. Write down the Kepler’s laws for planetary motion. 19. Define - (i) escape velocity (ii) geostationary satellite.
20. What is the value of escape velocity at earth surface? Will value of escape velocity change with change in projection angle.
UNIT II
Dynamics of Rigid Body (Rotational Motion): Rotational motion, Moment of inertia, Theorems of Perpendicular and Parallel axis of moment of inertia (Statement only). Radius of gyration, angular momentum, Conservation of angular momentum, Torque.
Friction : Introduction , Advantage and disadvantage of friction, Static and dynamic frictional forces. 1. What do you understand by rigid body?
2. What do you mean by moment of inertia of a rigid body?
3. Explain - (a) Radius of gyration (b) Theorem of parallel axis (c) Theorem of perpendicular axis. 4. Define- (a) Torque and (b) angular momentum.
5. Give some examples of torque in your daily life.
6. Obtain the relation between linear acceleration and tangential acceleration.
7. A body, initially at rest, is rotated by torque of magnitude 8 N-m. If torque remain acting on body for 20 s and moment of inertia of body is 4 kg-m2, then calculate the following- [PSK Pg. 141
Unsol.Ques. 22]
(i) Angular acceleration of a body. (ii) angular displacement
(iii) work done by torque
(iv) angular velocity after 20s (v) angular momentum of body after 20s
8. Derive the relationship between angular acceleration and torque of rotating body.
9. Drive the relation ¿d L/dt , between angular momentum (L) and moment of force (). 10. Explain the principle of conservation of angular momentum.
11. A particle of mass 2 kg is rotating in a circle of radius 1.5 m. Find the moment of inertia of the particle about axis of rotation. [PSK Pg. 122 Ex. 1] 12. A ring of mass 200 gm and radius 10 cm is rotating about its geometrical axis. Find out its moment of
inertia. What is the radius of gyration of ring? [PSK Pg 123 Ex. 5] 13. What is friction? Write the laws of friction.
14. Explain – (a) static friction (b) limiting friction (c) kinetic friction. 15. Distinguish between friction and limiting friction.
16. Write advantages and disadvantages of friction. 17. What do you mean by coefficient of friction?
18. A body of mass 5kg is resting on a horizontal plane. Coefficient of static friction is 0.3 between body and plane. Determine the minimum and maximum static friction. What is the magnitude of limiting friction? [PSK Pg.179 Ex1] 19. A block of mass 2 kg is resting on a horizontal plane. The coefficients of static and kinetic friction
between block and surface are 0.15 and 0.12 respectively. Calculate the minimum horizontal force required to move the block. [PSK Pg.184 Ex12] 20. A block of mass 2 kg is resting on a horizontal plane. Coefficient of static friction is 0.4 between block
and surface. A horizontal force of 2.5 N acts on the block. Find the force of friction between block and surface. [PSK Pg.181 Ex6]
UNIT III
Elasticity: - Elasticity, stress and strain. Hook’s law, elastic limit. Modulus of elasticity- Young's modulus, bulk modulus and modulus of rigidity.
Simple Harmonic Motion: Periodic Motion, characteristics of simple harmonic motion; equation of S.H.M. and determination of velocity and acceleration. Simple pendulum and Derivation of their periodic time.
1. Explain the terms - (a) elasticity (b) stress (c) strain 2. What do you mean by Hook’s law?
3. What do you understand by elastic limit of a material?
4. Explain the following terms- (a) Young’s modulus (b) bulk Modulus (c) Modulus of rigidity or shear modulus. (d) Poisson’s Ratio.
5. Find stress, strain and Young modulus of elasticity in the case of a wire 1.5 m long and 1 sq. mm in cross section, if it increases by 1.55 mm in length, when a weight of 10 kg is suspended from it.
[VJ Pg. 12.6 Unsol.Ques. 2]
6. A cube of aluminium of each side 4 cm is subjected to a tangential force. The top face of the cube is sheared through 0.012cm with respect to bottom face. Find (a) shearing strain (b) shearing stress (iii) shearing force. Given shear modulus η = 2.08 × 1011 dyne cm-2. [VJ Pg. 12.5 Ex.3]
7. Compute the bulk modulus of water from the following data: Initial vol. = 100 litre, pressure increase =100atm, final volume=100.5 litre (1atm = 1.013 ×105 Pa). [VJ Pg. 12.5 Ex.2]
8. Give some applications of elasticity.
9. What do you mean by Simple harmonic motion? 10. Define the following elements of the particle in S.H.M
(a) Frequency (b) Time Period (c) angular frequency (d) Displacement (e) amplitude (f) Phase. 11. Explain the term restoring force. What are the characteristics of S.H.M?
12. Write the equation for displacement of particle in simple harmonic motion. Using this equation derive the expression for velocity and acceleration of the particle executing S.H.M.
13. A body of mass 1 kg is executing simple harmonic motion according to the following equation x = 0.6 cos (100t +π/4) m. Determine
(a) amplitude of displacement, (b) frequency of oscillations, (c) initial Phase (d) maximum acceleration [PSK Pg. 214 Ex.1] 14. Eq. of displacement of a particle executing S.H.M is given by y = 0.1 sin π (t + 0.5) m. where time t is in
second. Determine amplitude, time period, maximum velocity, maximum acceleration and displacement of the particle at start of oscillations. [PSK Pg. 215 Ex.3] 15. What is simple pendulum? Find the expression T=2π
√
lg for the time period of simple pendulum.
16. Explain restoring force in detail.
17. Write down all the characteristics of SHM and their values at different intervals of a time period.
18. How does the time period of simple pendulum be affected when (i) mass of the bob is increased (ii) Simple pendulum is taken inside a satellite orbiting around earth.
19. A simple pendulum completes 25 oscillationsin eight minutes. Velocity of the bob at the lowest position is 50cm/s. Calculate the amplitude and acceleration of oscillations. [PSK Pg.217 Ex.7] 20. A simple pendulum is allowed to oscillate inside a lift. Lift is moving upward with 1.5 m/s2 acceleration. If
UNIT IV
Application of Sound
Waves:-Acoustics:- Definition of pitch, loudness, quality and intensity of sound; Echo, reverberation and reverberation time.
Optics: Quantum nature of light, Coherence, Duality of wave and particle; Elementary Concept of Interference, diffraction and polarization; Brewster’s law and Malus law.
1. What is sound wave? Differentiate between longitudinal and transverse wave. 2. Define pitch, loudness, quality and intensity of a sound wave?
3. Differentiate between Echo and reverberation.
4. A person is standing at 167 m distance from a tower. Person produces a sharp sound. If speed of sound is 334m/s and air is still, then find the time after which he listen echo. [PS K Pg. 302]
5. Write and drive Sabine’s formula for reverberation time.
6. Determine the reverberation time of an auditorium of volume 2200 m3 and total surface area m2. Assume
average coefficient of absorption for room as 0.15.[PSK Pg. 310 Ex.14]
7. What do you understand by Planck’s quantum theory? Explain dual nature of light?
8. What do you understand by De-broglie wavelength? Write the expression for momentum of the moving particle.
9. A source is emitting light of wavelength 6000 A0. Determine the frequency of light and energy associated
with a photon. Speed of light = 3×108 m/s and Planck’s constant h= 6.6 ×10-34 j-s.
[PSK Pg.318 Ex.1]
10. A particle is moving in space such that de Broglie wavelength associated with the particle is 0.1Ao.
Calculate momentum of the particle. h= 6.6 ×10-34 j-s. [PSK Pg.320 Ex.4]
11. What do you understand by coherent sources of light?
12. What do you mean by interference? Define the types of interference. 13. What are the essential conditions for the two light waves to be interfere?
14. What do you understand by (i) Diffraction of light and (ii) Polarization of light? 15. Explain the following terms –(i) plane of vibration (ii) plane of polarization.
16. With the help of neat diagrams differentiate between ordinary and plane polarized light.
17. What is Brewster’s law? Show that the reflected ray and refracted ray make 90 angles with each other. A⁰
light beam is incident on a medium of refractive index √3. If reflected light is completely plane polarized, then find the angle of polarization and angle of refraction.
[PSK Pg.344 Ex.29]
18. Explain the Malus law. Two polaroids are placed such that their axis make 30 angle with each other. If I⁰ 0
be the intensity of unpolarised light, then calculate the percentage intensity of transmitted light through second Polaroid. [PSK Pg.344 Ex.30]
19. A light beam is incident on a medium of refractive index √3. if reflected light is completely plane polarized, then find the angle of polarization and angle of refraction. [PSK Pg.344 Ex.30]
20. An α particle is moving with 106 m/s speed. Calculate the wavelength of α particle. Mass of α particle is 6.68 x 10-27 kg. [PKS Pg. 348 Unsol.Ques. 31]
UNIT V
Electrostatics: Electric Charges, Coulomb’s law-force between two point charges; Electric field, electric field due to a point charge; Electric flux, statement of Gauss’s theorem. Electric potential, potential difference, equi-potential surfaces.
Electrodynamics: Ohm’s law, Limitations of Ohm’s law, Ampere’s Law, faraday’s law, Biot- Savart’s Law. 1. Name the two kinds of electrical charges. Mention three properties of electrical charges.
2. Explain the term Quantization of charge.
3. State the Coulomb’s law of electrostatic force between the two charges. Using Coulomb’s law, calculate the force between a negative charge of 4 C and a positive charge of 6 C when placed 0.12 m apart. [VJ Pg. 23.4 Ex.1] 4. Define electric field. Derive an expression for electric field due to point charge at a distance r. 5. What are electric lines of force? List all the properties of electric lines of forces.
6. Define electric potential. Deduce the relation electric field and electric potential.
7. Derive an expression for electric potential due to point charge at a distance r from a point charge q. 8. Separate the scalar and vector quantities among the following (a) electric field (b) electric potential (c)
charge (d) electric flux (e) electromotive force.
9. 10 C of charge is uniformly distributed over the surface of sphere of radius 10 cm. Find electric field intensity at [VJ Pg. 23.18 Ex.13] (a) a point distant 20 cm from the centre of sphere
(b) at a point on the surface of sphere. (c) at a point 5 cm from the centre of sphere.
10. Calculate the electric potential at the surface of the silver nucleus having radius 3.4 × 10-14 m. The
atomic no. silver is 47 and charge on the proton = 1.6 × 10-19 C. [VJ Pg. 23.28 Ex.18]
11. Write the magnitude of electrical permeability of free space, ε0. Can Two electric lines of force cross
each other.
12. Define potential difference. A point charge of 1 C is placed between points A and B 3m apart. Point A is 2 m from the charge and B is 1 m from the charge. What is the potential difference VA-VB?
[VJ Pg. 23.23 Ex.14] 13. Calculate the intensity of electric field due to a point charge of 10 C at 10 cm from the charge.
[PSK Pg. 404 Unsol. Ques. 25]
14. State the following - (a) Gauss’s theorem (b) Equi-potential surface
15. Three charges +3, -4, +6 C are placed inside a sphere. Find the magnitude and direction of the flux passing through the sphere. [VJ Pg. 23.15 Ex.10] 16. State and explain Biot and Savart’s law. Apply Biot and Savart’s law to determine the magnetic field
due to a steady current I in a long straight wire.
17. Define Ohm’s law. What are the limitations of ohm’s law? A battery has an emf of 12.8 volts. What is the resistance of the circuit? How many coulombs leave the battery in 5 minutes? [VJ Pg. 24.5 Ex.2] 18. An electric iron of 105.8 ohm when connected across supply mains draws 2.174 ampere current. What
is the value of supply voltage.
19. State and explain Faraday’s law. If the magnetic flux passing through the coil of 100 turns increases 15 weber in 2 seconds then determine the induced emf in the coil.
20. Define Ampere’s circuital Law. Calculate the magnetic flux density at the centre of the solenoid of 2000 turns and 50cm long if a current of 0.5 A flows in the coil. [VJ Pg. 25.14 Ex.5]
1. Kushwaha P. S., Applied Physics, Bharat BhartiPublications, Meerut.
