**Some Important long questions**

**PHYSICS by Note Library**

**Mechanics:**

1. What is simple pendulum? Show that motion of the bub of the simple pendulum is simple harmonic and hence obtain an expression for its time period.

2. Define SHM. Derive a relation for total energy of a simple harmonic oscillator. How do K.E., P.E. and T.E vary with position?

3. Define SHM. Show that the oscillation of mass suspended from helical spring is simple harmonic and hence find the expression for its time period.

4. Define angular simple harmonic motion. Show that motion of the balance wheel is angular simple harmonic and hence obtain an expression for its time period.

5. What is meant by moment of inertia? How is it related with the rotational kinetic energy of a body?

6. What do you mean by a rigid body? Obtain an expression for the moment of inertia of a thin and uniform rod about an axis passing through (i) the centre and perpendicular to its length & (ii) one of its ends and perpendicular to its length.

7. Derive a relation between torque applied with angular acceleration produced in a rigid body and moment of inertia.

8. Derive the relation between angular momentum and moment of inertia of a rigid body.

9. State and explain the principle of conservation of angular momentum.

10. Define the terms: couple and moment of a couple. Derive an expression for the work done by a couple.

11. Define surface tension and surface energy of a liquid and derive a relation between them.

12. What is capillarity? Derive an expression for the rise or fall of liquid in a capillary tube.

13. What is terminal velocity? Derive an expression for terminal velocity of a small spherical ball of radius 'a' dropped gently in a viscous liquid of density 'σ' and coefficient of viscosity.

14. State and prove Bernoulli's theorem for flow of non-viscous fluids.

15. Derive Newton’s formula for viscus force. Define coefficient of viscosity. Also find its dimensional formula.

16. Using dimensional method, deduce Poiseulle’s formula for the rate of flow of a liquid through a tube.

Electricity and Magnetism:

17. What do you mean by a shunt? Describe its use in converting a galvanometer into an ammeter.

18. What is a galvanometer? How can you convert it into voltmeter? Why should the resistance of a voltmeter be high?

19. State and explain Joule's law of heating of electric current. Deduce an expression for the heat developed in a wire by the passes of electric current?

20. State and explain Kirchhoff’s laws of current and voltage. Explain how these laws are used to obtain the balanced condition of Wheatstone’s bridge.

21. What is a Wheatstone bridge? Obtain the balanced condition for the bridge. Explain how resistance can be measured by a meter bridge.

22. Discuss the principle of the potentiometer and use it to compare the emf's of two cells.

23. Discuss the principle of potentiometer and use it to determine the internal resistance of a cell.

24. Explain what do you mean by Seebeck Effect? How does thermoelectric e.m.f. vary with the temperature? Derive the relation between thermoelectric constants.

25. Derive an expression for force on a current carrying conductor placed in uniform magnetic field.

26. State Biot-Savart law. Derive the formula for the magnetic field at the centre of a circular coil carrying current. Explain why the magnetic field at the centre of the coil disappears when the circular coil is made infinitely large.

27. State Biot-Savart law. Derive an expression for the magnetic field produced by a current carrying circular coil at any point on the axis of the coil.

28. Derive the formula for the magnetic field at a point due to a long straight current carrying conductor using Biot- Savart law.

29. Using Biot-Savart law, derive an expression for magnetic field intensity due to a long solenoid.

30. Derive the formula for the magnetic field at a point due to a long straight current carrying conductor/Toroid using Ampere's law.

31. State and explain Ampere's theorem and hence use it to find the magnetic field intensity due to a long current carrying solenoid.

32. Derive an expression of force per unit length between two parallel conductors separated by a distance ‘r’ and carrying currents I1 and I2 in the same/opposite direction.

33. Find an expression for torque on rectangular coil in a uniform magnetic field.

34. Describe with the help of a diagram, the principle, construction and working of a moving coil galvanometer.

35. What is Hall Effect? Derive an expression for Hall voltage and Hall coefficient.

36. State Faraday's law of electromagnetic induction. Derive an expression for the e.m.f. induced in a straight conductor moving at right angle to the direction of a uniform magnetic field.

37. State and explain Faraday's law of electromagnetic induction. Derive an expression for the emf induced in a coil rotating in a uniform magnetic field.

38. State Lenz's law and explain how this law leads to the conservation of energy principle.

39. Describe the theory and working of an a.c. generator.

40. Define self-inductance and find its relation with magnetic flux and current, also derive an expression for it (factors affecting self-inductance).

41. Define mutual-inductance and find its relation with magnetic flux and current, also derive an expression for it (factors affecting mutual-inductance).

42. Define self-inductance. Derive an expression for energy stored in an inductor.

43. An alternating emf is applied across a capacitor. Show that the current in it leads to the applied emf by 90°.

44. Discuss the phase relationship between the voltage and current in the AC circuit containing inductance and resistance. What is power factor of the circuit?

45. Discuss the phase relationship between the voltage and current in the a.c. circuit containing capacitor and resistor in series and hence derive an expression for the impedance of the circuit.

46. Derive the expression for impedance and current in LCR series circuit. Also find the resonant frequency.

**Thermodynamics**:

47. Why does a gas have two molar heat capacities? Show that for an idea gas CP - Cv = R, where is the molar gas constant.

48. Define adiabatic process in thermodynamics. Show that PV^Γ= constant, where symbols have their usual meanings.

49. What is adiabatic process? Derive an expression for work done in adiabatic system.

50. What is reversible and irreversible process? Derive an expression for the work done by an ideal gas during Isothermal expansion.

51. Describe the working of petrol engine with the help of P-V, diagram.

52. State and explain second law of thermodynamics. Explain the working of a diesel engine on P - V diagram and write down its merits and demerits.

53. Describe the working of Carnot engine with the help of a P-V diagram.

**Wave & Sound**

54. What are stationary waves? Prove that the distance between any two consecutive nodes in a stationery wave is λ/2.

55. Differentiate between progressive and stationary wave. Derive an equation for a progressive wave.

56. What is the Newton's formula for the velocity of sound? What correction was made by Laplace?

57. Derive an expression for the velocity of sound in a medium by dimensional method. Discuss the effect of various factors on the velocity of sound in air.

58. What do you understand by 'harmonics' and 'overtone' in the case of organ pipe? Also prove that only odd harmonics are produced in closed ended organ pipe.

59. Show the both harmonics, odd and even can be produced in an open organ pipe. What is end correction?

60. Define the intensity of sound and prove that I= 1/2 ρva^2w^2=1/2 √rB w^2a^2 ,where the symbols have their usual meaning.

61. Discuss the phenomenon of Doppler's effect. Derive an expression for the change in frequency

(i) when a moving source of sound passes a stationary observer. (ii) when an observer and source both are approaching each other. (iii) when an observer moves towards a stationary source and then moves away from the source.

**Optics:**

62. State and explain Huygen's principle. Use the principle to show that a plane wave front incident obliquely on a plane mirror is reflected as a plane wave front so that the angle of incidence is equal to the angle of reflection.

63. Define Huygen's principle and prove Snell's law by the help of wave theory of light.

64. What do you mean by constructive and destructive interference of light? Prove analytically that the bright and dark fringes in young's double slit experiment are equally spaced.

65. What is Fraunhofer diffraction? Explain the formation of maxima and minima due to diffraction? Show that the width of central maxima is inversely proportional to the distance between the two slits.

66. What is polarizing angle? State and prove Brewster’s law. Also explain the applications of Brewster’s law.

**Modern Physics:**

67. Describe with necessary theory, Millikan's oil drop experiment to determine the value of the charge associated with an electron.

68. Show that the motion of an electron in magnetic field is circular. Prove that frequency and time period are independent with the velocity of an electron.

69. What is specific charge of an electron? Describe and give necessary theory of J.J. Thomson's method to determine the specific charge of an electron.

70. What is photoelectric effect? Derive Einstein’s photoelectric equation; define various terms used in it.

71. Describe Millikan's experiments to verify Einstein's photoelectric equation and hence determine the value of Plank’s constant.

72. What is an extrinsic semiconductor? Explain the formation of potential barrier and depletion region in a p-n junction diode.

73. Explain with neat diagram, the working mechanism of a full wave rectifier using junction diodes. How the output changes when a filter circuit is used?

74. What if junction diode? Explain its working as half wave rectifier.

75. What is Zener breakdown? Describe how a Zener diode can be used as a voltage regulator?

76. What are Bohr's postulates of hydrogen atom? Derive an expression for the radius of Bohr's nth orbit.

77. Starting from Bohr's postulates, obtain an expression for the energy of the electron in nth orbit of the hydrogen atom.

78. Describe the modern method of productions of X-rays. Discuss crystal diffraction.

79. Derive Bragg's law and explain how this law is used to determine the crystal plane spacing.

80. State laws of radioactive disintegration and show that the number of atoms of a given radioactive substance decreases exponentially with time. Also, derive a relation between decay constant and half-life of a radioactive substance.

**Recent trends in physics:**

81. What are hypocenter and epicenter? Discuss the origin of earthquake. Write the difference between main shock and after shock.

82. What is seismology? What are the difference between lithosphere and asthenosphere? What are the safety measures of earth quake?

83. Why does p-wave travel faster than s-wave? What is the cause and effect of Gorkha earthquake?

84. What is nano-technology? Discuss different aspects of nano-technology. Give the concept of Higg’s boson with dark meter.