PHYSICS PAPER- 1
(i) Write an expression (derivation not required) for intensity of electric field in:
(1) Axial position.
(2) Broad side position of an electric dipole, in terms of its length (2a) dipole moment
(p) and distance (r).
(ii) What is the ratio of these two intensities i.e. El: E2, for a short electric dipole?
(Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time. )
------------------------------------------------------------------------------------------------------------Answer all questions in Part I and six questions from Part II, choosing two questions from each of the Sections A, B and C.All working, including rough work should be done on the same sheet as, and adjacent to, the rest of the answer.The intended marks for questions or parts of questions are given in brackets [].------------------------------------------------------------------------------------------------------------
Part I (20 Marks)
Question 1
A. Choose the correct alternative (a), (b), (c) or (d) for each of the questions given below:
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This Paper Consists Of 10 Printed Pages.
(ii) Five resistors are connected as Shown in Figure 1
The effective resistance i.e. equivalent resistance between the points A and B is:
(a) 4 Ω
(b) 5 Ω
(c) 15 Ω
(d) 20 Ω
(iii) The Biot Savart's Law in vector form is:
(iv) In an astronomical telescope of refracting type:
(a) Eyepiece has greater focal length.
(b) Objective has greater focal length.
(c) Objective and eyepiece have equal focal length
(d) Eyepiece has greater aperature than the objective.
(v) The particles which cannot be accelerated by a cyclotron or a Van de Graff
generator are:
(a) Alpha particles
(b) Beta particles
(c). Neutrons
(d) Protons
B. Answer all questions given below briefly and to the point:
(i) A large hollow metallic sphere has a positive charge of 35.4μ C at its center
Find how much electric flux emanates from the sphere.
(ii) A current 'I' flows through a metallic wire of radius 'r' and the free electrons in it
drift with a velocity Vd. Calculate the drift velocity of the free electrons through the
wire of the same material, having double the radius, when same current flows through it.
(iii) Name anyone instrument which works on the principle of tangent law in magnetism.
(iv) State die SI Unit of magnetic dipole moment.
(v) Alternate current flowing through a certain electrical device leads over the potential
difference across it by 90°. State whether this device is a resistor, capacitor or an inductor.
(vi) What is the shape of the wavefront diverging from a point source of light?
(vii) The critical angle for a given transparent medium and air is ic . A ray of light
traveling in air is incident on this transparent medium at an angle of incidence equal
to the polarising angle ip . What is the relation between the two angles ic and ip ?
(viii) Find the focal length and nature of a lens whose optical power is - 5D.
(ix) What is Modulation? Explain in brief.
(x) What are the dark lines seen in the solar spectrum called?
(xi) What is be relation between wavelength and momentum of moving particles?
(xii) Name the series of lines in the hydrogen spectrum which lies in the ultra-violet region.
(xiii) Fill in the blank in the given nuclear reaction:
(xiv) Give an example where energy is converted into matter.
(xv) To convert a pure semiconductor into n-type semiconductor, what type of impurity is
added to it?
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Part II (50 Marks)
Answer six questions in this part, choosing two questions from each of the Sections A, B and C. SECTION A Answer an we questions.
Question 2.
(a)
(1) Axial position.
(2) Broad side position of an electric dipole, in terms of its length (2a) dipole moment
(p) and distance (r).
(ii) What is the ratio of these two intensities i.e. El: E2, for a short electric dipole?
Calculate:
(i) Charge on each plate of capacitor C1
(ii) Electrostatic potential energy stored in capacitor C3.
(c) 'n' cells, each of emf 'e' and internal resistance 'r' are joined in series to form a row.
'm' such rows are connected in parallel to form a battery of N = mn cells. This battery is
connected to an external resistance 'R'.
(i) What is the emf of this battery and how much is its internal resistance?
(ii) Show that current 'I' flowing through the external resistance 'R' is given by:
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Question 3
(a) In the circuit shown in Figure 3, E1 =17 V, E2 = 21 V, R1 = 2 Ohm, R2 = 3 Ohm and R3 =5 Ohm.
Using Kirchoff's laws, find the currents flowing through the resistors R1, R2 and R3.
(Internal resistance of each of the batteries is negligible.)
(b) You are provided with one low resistance RL and one high resistance RH and two
galvanometers. One galvanometer is to be converted to an ammeter and the other to a
voltmeter. Show how you will do this with the help of simple, labelled diagrams.
(c)
(i) Plot a labelled graph to show variation of thermo-emf 'e' versus temperate difference 'θ'
between the two junctions of a thermocouple. Mark 'N' as neutral temperature and 'I' as
temperature of inversion.
(ii) What is Peltier effect?
Question 4
(a) Figure 4 below shows two infinitely long and thin current carrying conductors X and Y
kept in vacuum, parallel to each other, at a distance 'a'.
(i) How much force per unit length acts on the conductor Y due to the current flowing
through X ? Write your answer in terms of (µ0/4π), I1,I2 and a.
(Derivation of formula is not required.)
(ii) Define ampere, in terms of force between two current carrying conductors.
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(b) A metallic rod CD rests on a thick metallic wire PQRS with arms PQ and RS parallel to
each other, at a distance l = 40 cm, as shown in Fig 5. A uniform magnetic field
B = 0.1T acts perpendicular to the plane of this paper, pointing inwards (i.e. away from
the reader). The rod is now made to slide towards right, with a constant velocity of v= 5.0 m/s.
(i) How much emf is induced between the two ends of the rod CD ?
(ii) What is the direction in which the induced current flows?
(c)
(i) Figure 6 below shows a series RCL circuit connected to an ac source which
generates an alternating emf of frequency 50 Hz. The readings of the voltmeters
V1 and V2 are 80 V and 60 V respectively.
Final:
(1) the current in the circuit.
(2) the capacitance C of the capacitor
(ii) At resonance, what is the relation between impedance of a series LCR circuit and
its resistance R?
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SECTION B
Answer any TWO questions
Question 5
(a)
(ii) How long would gamma radiation take to travel from sun to earth, a distance of 1.5x10^11m?
(b) With the help of a labelled diagram, show that fringe separation Young's double slit experiment is given by:
where the terms have their usual meaning.
(c) (i) What is the difference between polarized light and unpolarized light based on the direction of electric vector ( E ) ?
(ii) What will be the effect on the width of the central bright fringe in diffraction pattern of a single slit if:
1) Monochromatic light of smaller wavelength is used.
2) Slit is made narrower.
Question 6
(a) At what angle, a ray of light should be incident on the first face AB of a regular glass prism ABC so that the emergent ray grazes the adjacent face AC ? See Figure 7 below.
(Refractive Index of glass = 1 6)
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b) A convex lens 'L' and a plane mirror 'M' are arranged as shown in Figure 8 below.
Position of object pin 'O' is adjusted in such a way that the inverted image 'I' formed by the lens mirror combination, coincides with me object pm 'O'. Explain how and when this happens.
(c) Starting with an expression for refraction at a single spherical surface, obtain an
expression for lens maker's formula.
Question 7
(a) Show that the axial chromatic aberration (fr - fv ), for a convex lens is equal to the
product of its mean focal length (f) and dispersive power (w) of its material i.e. Prove:
(b) Draw a labelled diagram of an image formed by a compound microscope, with the image at least distance of distinct vision. Write any oneexpression for its magnifying power.
(c) What is meant by long-sightedness? How can this defect be corrected?
SECTION C
Answer any two
Question 8
(a) (A What is meant by 'Quantization of chased'?
(ii) In Thomson's experiment, prove that the ratio of charge to the mass (e/m) of an
electron is given by:
where the terms have their usual meaning.
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((b) In a photoelectric cell, a retarding potential of 0.5V is requested to block the movement
of electrons from the cathode when monochromatic light of wavelength 400 nm is
incident on its surface. Find the work function of the material of the cathode.
(c) Name a phenomenon or an experiment which proves:
(i) Particle nature of electromagnetic radiations.
(ii) Wave nature of particles. (Description of the phenomenon / experiment is not require.)
Question 9
(a) (i) State thee postulate of Bohr's theory regarding-:
(1) Angular momentum of an electron.
(2) Emission of a photon.
(ii) Total energy of an electron orbiting around the nucleus of an atom is always negative. What is the significance of this?
(b) (i) Draw a labelled graph showing variation of relative intensity of X-rays versus their wavelength
of lambda. Mark lambda min on the graph. A. Mark gamin on the graph.
(ii) State how the value of Lambda min can be varied.
(c) Half life of a certain radioactive substance is 6 hours. If yo~ad 3.2kg of this substance in the beginning, how much of it will disintegrate in one day?
Question 10
(a) (i)What is the significance of binding energy per nucleon of a nucleus?
· (ii) In a certain star, three alpha particles undergo fusion in a single reaction to form Carbon 12 nucleus. Calculate the energy released in this reaction in MeV
Given: Mass of one helium = 4.002604 u and mass of one Carbon 12 = 12.000000 u.
(b) Show by drawing labelled diagrams, the nature of output voltages in case of:
(i) A half wave rectifier.
(ii) A full wave rectifier.
(iii) An Amplifier. (In each case, input is an ac voltage)
Circuit diagrams of these devices are not required.
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(c) Identify logic gate whose truth table is given below and draw its symbol:
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