b.sc physics paper i

Paper-I: Mechanics, waves and oscillations

List of Important Questions

UNIT-I

Vector Analysis

Essay Questions

1. What is divergence of a vector field and obtain expression for the divergence of a vector. Give its significance. Define the line integral, surface integral and volume integral of a vector quantity. State and prove Gauss divergence theorem.

2. What is curl of a vector field derive an expression for curl of a vector. Give its physical significance.

3. State and prove Stoke’s theorem. By Stoke’s theorem, prove that the curl of gradient of scalar function is zero.

Short Answer Questions

1. State and prove Green’s theorem.2. Define gradient of a scalar field. Explain its physical significance.3. Explain the physical significance of a curl.4. Explain the terms line integral, surface integral and volume integral.5. Explain the different types of vector fields with examples.

Problems

1. If F=2xi+5yj+6zk, using Gauss divergence theorem, show that

Mechanics of Particles

Essay Questions

1. Describe the motion of a variable mass system and derive the equation for the velocity of a rocket under the influence of gravitational field.

2. Define the terms impact parameter and scattering cross section. Derive an expression for Rutherford’s scattering angle.

3. What are elastic and inelastic collisions. Derive an expression for the scattering cross section in the case of alpha particles striking the gold foil in Rutherford scattering experiment.


1. Explain the terms “ impact parameter” and “scattering cross section”2. Derive the expression for the velocity of rocket at any time, treating it as a variable

mass system.3. Distinguish between elastic and inelastic collisions with examples.4. Explain the principle of multistage rocket.

Problems

Mechanics of Rigid Bodies

Essay Questions

1. Define the terms “Rigid body” and “Moment of Inertia”. Obtain Euler’s equation of motion of a rigid body. Deduce the law of conservation of energy and angular momentum from Euler’s equations.

2. Explain the precession of symmetric top. Obtain an expression for its torque.3. What is meant by rigid body? Obtain an expression for the motion of a rigid body

rotating about the axis of symmetry.4. Define radius of gyration .Derive the expression for the kinetic energy of a rotating

body. State and prove work energy theorem in rotational motion.


1. Write a note on “Inertia tensor”.2. Write briefly about gyroscope.3. Deduce conservation of angular momentum from Euler’s equations.4. Explain the principle of gyroscope and its uses.5. Obtain the equation of for a rotating body.

Problems

UNIT-II

Mechanics of Continuous media

Essay Questions

1. Explain the types of beams and types of bending. Derive an expression for the depression of the free end of a cantilever fined at one end and loaded at the free end.

2. Explain the uniform and non-uniform bending of beams. Express Poisson’s ratio in terms of the elastic modulii Y, n and k. What are the limits of Poisson’s ratio?


1. Obtain the relation (Y/3k) +(Y/n) =3, where Y is Young’s modulus, k is Bulk modulus and n is rigidity modulus.

2. Define Poisson’s ratio. Discuss its limiting values.3. Define and explain the three elastic modulii.4. Give a brief account of the classification of beams.

Problems

Central forces

Essay Questions

1. Solve the equation of motion of a particle in an inverse square force field. Derive Kepler’s laws.

2. What is central force? Derive the equation of motion of a particle under the action of central force.

3. State and prove Kepler’s laws of planetary motion. Derive the condition under which the path of a planet around the sun is an ellipse.


1. What are central forces? Give three examples. Show that central forces are conservative.

2. What is a central force? Deduce the relation between a conservative force and the potential energy.

3. State Kepler’s second law and show that the real velocity of the planet remains constant.

4. Write a short note on Coriolis force.

Problems

Special Theory of Relativity

Essay Questions

1. What is Ether hypothesis? Describe Michelson Morley experiment and discuss the significance of the results. (Explain the negative result).

2. What is frame of reference? Derive Lorentz transformation equations.3. State and explain Einstein’s postulates of the special theory of relativity and deduce

mass-energy theorem.


1. Explain length contraction and time delation.2. Deduce mass-energy equivalence relationship.3. State Lorentz transformation equations and inverse Lorentz transformation equations.4. Explain length contraction and time delation.5. Explain the concept of four vector formalism.6. Derive the energy momentum relation based on the special theory of relativity.

Problems

UNIT-III

Fundamentals of Vibrations

Essay Questions

1. Explain the physical characteristics of simple harmonic motion. Describe the equation of motion for a simple harmonic oscillator and obtain its solution. Show that the total energy of the oscillator is proportional to the square of the amplitude.

2. Discuss the linear combination of two mutually perpendicular simple harmonic vibrations of different frequencies.

3. Define Lissajous figures. Discuss the effect of combining simple harmonic motions of same frequencies acting at right angles to each other.


1. Explain “Lissajous Figures”.2. Derive the equation for time period of a torsional pendulum.3. Derive an expression for vibration energy of an oscillator.4. Explain the physical characteristics of simple harmonic motion.5. Derive the expression for the frequency of vibration of a spring taking its mass into

consideration.

Problems

Damped and Forced Oscillations

Essay Questions

1. Distinguish between damped and un damped vibrations of a simple oscillator. Obtain the differential equation and discuss the solution under different conditions. Discuss its energy considerations and logarithmic decrement in amplitude.

2. What are forced vibrations? Setup the equation of motion for a forced oscillator and discuss its solution. Obtain an expression for the amplitude of forced vibrations and deduce the condition for resonance.


1. What is “Quality factor”? Discuss its importance.2. Write a short note on Amplitude resonance.3. What is “transverse impedance”?4. Explain the terms logarithmic decrement and relaxation time. How to correct the

logarithmic decrement. 5. Explain the terms resonance, sharpness of resonance and quality factor.6. Explain how the sharpness of resonance is affected by quality factor (Q-factor).

Problems

Complex Vibrations

Essay Questions

1. Explain how Fourier theorem can be used for analysis of a complex wave. Analyse a saw-tooth wave using Fourier theorem.

2. State Fourier theorem and evaluate the Fourier coefficients. Using Fourier theorem analyse a triangular wave.

3. State Fourier’s theorem. What are its limitations? Find the Fourier series for the function of (t) denoted by Y = +a when 0<t<T/2 and y = -a when T/2<t<T


1. State the conditions under which Fourier theorem is applicable.

Problems

UNIT-IV

Vibration of Bars

Essay Questions

1. Find the equation of motion for a longitudinal wave in a bar. Discuss its solution in different cases as given below.(i) When both ends are free(ii) When one end is fixed

2. Derive the transverse wave equation in a bar. Derive the general solution for the transverse wave equation in a bar.

3. Discuss the transverse vibrations in a bar free at both ends (free-free bar).


1. Discuss the vibrations of a tuning fork.2. Discuss briefly the longitudinal modes of vibration of a bar clamped at the centre.3. Compare between longitudinal and transverse vibrations in a bar.

Problems

Vibrating Strings

Essay Questions

1. What are transverse waves? Obtain the equation for the frequency of vibration in a stretched string. What are fundamental frequency and overtones? (Discuss the modes of vibration of stretched string clamped at both ends.)

2. Discuss the energy transport in the strings and obtain an expression for energy density.


1. State the laws of transverse vibrations of a string.2. Distinguish between the harmonics and overtones.3. Obtain an expression for the energy density of a wave travelling along a string.4. Distinguish between progressive and stationary waves.

Problems

Ultrasonics

Essay Questions

1. Describe the Sear’s method of finding the velocity of Ultrasonics in liquids. Mention different applications of ultrasonics.

2. What are ultrasonic and infrasonic waves? Describe how ultrasonic waves are produced by piezoelectric and magnetostriction method.


1. Write any ofour applications of ultrasonics.2. Explain a method of producing ultrasonics.3. Explain SONAR and its uses.4. Define the terms Magnetostriction and Piezoelectric effect5. Explain any four methods of detection of ultrasonic waves.

Problems

b.sc physics paper i

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