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Board Paper of Class 12-Science 2011 Physics (SET 3) - Solutions

General Instructions:
(i) All questions are compulsory.
(ii) There are 30 questions in total. Question Nos. 1 to 8 are very short answer type questions and carry one mark each.
(iii) Question Nos. 9 to 18 carry two marks each, question 19 to 27 carry three marks each and question 28 to 30 carry five marks each.
(iii) There is no overall choice. However, an internal choice has been provided in one question of two marks; one question of three marks and all three questions of five marks each. You have to attempt only one of the choice in such questions.
(iv) Use of calculators is not permitted.
  • Question 1

    A hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 5 V. What is the potential at the centre of the sphere?

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  • Question 3

    Define electric dipole moment. Write its S.I. unit.

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  • Question 4

    Where on the surface of Earth is the angle of dip zero?

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  • Question 5

    Define the term ‘stopping potential’ in relation to photo-electric effect.

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  • Question 6

    Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’ as shown in the figure. Predict the polarity of the capacitor.

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  • Question 7

    Write any two characteristic properties of nuclear force.

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  • Question 8

    What happens to the width of depletion player of a p-n junction when it is (i) forward biased, (ii) reverse biased?

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  • Question 9

    (i) Net capacitance of three identical capacitors in series is 2 μF. What will be their net capacitance if connected in parallel?

    (ii) Find the ratio of energy stored in the two configurations if they are both connected to the same source.

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  • Question 10

    In the meter bridge experiment, balance point was observed at J with AJ = l.

    (i) The values of R and X were doubled and then interchanged. What would be the new position of balance point?

    (ii) If the galvanometer and battery are interchanged at the balance position, how will the alance point get affected?

     

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  • Question 11

    Write the expression for Lorentz magnetic force on a particle of charge ‘q’ moving with velocity in a magnetic field. Show that no work is done by this force on the charged particle.

    OR

    A steady current (I1) flows through a long straight wire. Another wire carrying steady current (I2) in the same direction is kept close and parallel to the first wire. Show with the help of a diagram how the magnetic field due to the current I1 exerts a magnetic force on the second wire. Write the expression for this force.

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  • Question 12

    State the principle of working of a transformer. Can a transformer be used to step up or step down a d.c. voltage? Justify your answer.

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  • Question 13

    Using the curve for the binding energy per nucleon as a function of mass number A, state clearly how the release in energy in the processes of nuclear fission and nuclear fusion can be explained.

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  • Question 14

    In the given circuit, assuming point A to be at zero potential, use Kirchhoff’s rules to determine the potential at point B.

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  • Question 15

    Plot a graph showing the variation of coulomb force (F) versus , where r is the distance between the two charges of each pair of charges: (1 μC, 2 μC) and (2 μC, − 3 μC). Interpret the graphs obtained.

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  • Question 16

    A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere’s circuital law is generalized to incorporate the effect due to the displacement current.

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  • Question 17

    What is ground wave communication? On what factors does the maximum range of propagation in this mode depend?

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  • Question 18

    A thin straight infinitely long conducting wire having charge density λ is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.

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  • Question 19

    A compound microscope uses an objective lens of focal length 4 cm and eyepiece lens of focal length 10 cm. An object is placed at 6 cm from the objective lens. Calculate the magnifying power of the compound microscope. Also calculate the length of the microscope.

    OR

    A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find the angular magnification of the telescope. If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.42 × 106 m and the radius of the lunar orbit is 3.8 × 108 m.

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  • Question 20

    (a) Using de Broglie’s hypothesis, explain with the help of a suitable diagram, Bohr’s second postulate of quantization of energy levels in a hydrogen atom.

    (b) The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?

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  • Question 21

    You are given a circuit below. Write its truth table. Hence, identify the logic operation carried out by this circuit. Draw the logic symbol of the gate it corresponds to.

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  • Question 22

    A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in (i) a medium of refractive index 1.6, (ii) a medium of refractive index 1.3.

    (a) Will it behave as a converging or a diverging lens in the two cases?

    (b) How will its focal length change in the two media?

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  • Question 23

    Write briefly any two factors which demonstrate the need for modulating a signal. Draw a suitable diagram to show amplitude modulation using a sinusoidal signal as the modulating signal.

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  • Question 24

    Draw a labeled diagram of a full wave rectifier circuit. State its working principle. Show the input-output waveforms.

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  • Question 25

    Two heating elements of resistances R1 and R2 when operated at a constant supply of voltage, V, consume powers P1 and P2 respectively. Deduce the expressions for the power of their combination whey they are, in turn, connected in (i) series and (ii) parallel across the same voltage supply.

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  • Question 26

    Use the mirror equation to show that

    (a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

    (b) a convex mirror always produces a virtual image independent of the location of the object.

    (c) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

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  • Question 27

    Draw a plot showing the variation of photoelectric current with collector plate potential for two different frequencies, v1 > v2, of incident radiation having the same intensity. In which case will the stopping potential be higher? Justify your answer.

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  • Question 28

    State the working of a.c. generator with the help of a labeled diagram.

    The coil of an a.c. generator having N turns, each of area A, is rotated with a constant angular velocity ω. Deduce the expression for the alternating e.m.f. generated in the coil.

    What is the source of energy generation in this device?

    OR

    (a) Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase. 

    (b) A horizontal straight wire of length L extending from east to west is falling with speed v at right angles to the horizontal component of Earth’s magnetic field B. 

    (i) Write the expression for the instantaneous value of the e.m.f. induced in the wire. 

    (ii) What is the direction of the e.m.f.?

    (iii) Which end of the wire is at the higher potential?

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  • Question 29

    State the importance of coherent sources in the phenomenon of interference.

    In Young’s double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence deduce the expression for the fringe width.

    How does the fringe width get affected, if the entire experimental apparatus of Young is immersed in water?

    OR

    (a) State Huygen’s principle. Using this principle explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a narrow beam coming from a monochromatic source of light is incident normally.

    (b) Show that the angular width of the first diffraction fringe is half of that of the central fringe.

    (c) If a monochromatic source of light is replaced by white light, what change would you observe in the diffraction pattern?

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  • Question 30

    (a) State the principle of the working of a moving coil galvanometer, giving its labeled diagram.

    (b) “Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.” Justify this statement.

    (c) Outline the necessary steps to convert a galvanometer of resistance RG into an ammeter of a given range.

    OR

    (a) Using Ampere’s circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis.

    (b) In what respect is a toroid different from a solenoid? Draw and compare the pattern of the magnetic field lines in the two cases.

    (c) How is the magnetic field inside a given solenoid made strong?

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