Physics (Theory)-2008

Code No. 55/1/2

 

Time Allowed: 3 hours]                                                [Maximum Marks: 70

 

1.         Name the part of the electromagnetic spectrum of wavelength 102 m and mention its one application.

 

1.         l = 102 m

            n = c/l = Hz

            \         radio wave, it is used in radar.

 

2.         An electron and alpha particle have the same kinetic energy. How are the de-Broglie wavelengths associated with them related?

2.         mv =  Þ lb =

            Kinetic energy    K =

           

           

            Since ma > me

             =

            Þ       

           

 

3.         A converging lens of refractive index 1.5 is kept in a liquid medium having same refractive index. What would be the focal length of the lens in this medium?

 

3.                     and 

            (Here mL = mm)

            Hence  Þ fm ® ¥.

 

4.         A 500 mC  charge is at the centre of a square of side 10 cm. Find the work done in moving a charge of 10 m C between two diagonally opposite points on the square.

 

4.         a = 0.1 m

            Q = 500 ´ 10-6 C

We have to find out work done to take a charge 10mC from A to C

DW = (q) (VC - VA)

q = 10 ´ 10-6C

Here VC and VA are electric potential at C and A due to charge (Q) placed at the centre

Since VA = VC

Þ        DW = 0.

 

5.         The plot of the variation of potential difference across a combination of three identical cells in series, versus current is as shown below. What is the emf of each cell?

           

5.        

           

            i =   

           

             = iR

            When i = 0, Vmax = 6V at R ® ¥

                        3E = 6

 \ E = 2V.

 

 

6.         How does the angular separation of interference fringes change, in Young’s experiment, if the distance between the slits is increased?

 

6.        

           

 

            Angular separation q = y/D =

            If d increases angular separation decreases.

 

7.         What is the direction of the force acting on a charged particle q, moving with a velocity  in a uniform magnetic filed ?

 

7.        

            Force is perpendicular to both magnetic field vector and velocity vector, which is in the direction of ( as right hand rule for positive charge.

 

8.         State the reason, why heavy water is generally used as a moderator in a nuclear reactor.

 

8.         Heavy water is used is to slow down the fast moving neutrons which are released during nuclear reaction. Due to collision between moving neutron and heavy water molecule, neutrons come to rest. Because it is an elastic collision with approx. equal mass.

 

9.         A nucleus  undergoes b-decay and becomes . Calculate the maximum kinetic energy of electrons emitted assuming that the daughter nucleus and anti-neutrino carry negligible  kinetic energy.

           

 

9.        

            Mass defect = Dm = 22.994466  - 22.989770

                        = 0.004696 u

            Energy released = Dm (in u) ´ 931.6 MeV

                        = 4.37 MeV, which in form of maximum K.E. of electron emitted.

 

10.       Distinguish between an intrinsic semiconductor and P-type semiconductor. Give reason, why a P-type semiconductor crystal is electrically neutral, although nh >> ne?

 

10.      

Instrinsic semiconductor

P-type semiconductor.

(1) It is pure form of semiconductor

(1) It is a impure form of semiconductor

(2) There is no use of intrinsic semiconductor

(2) It is useful in semiconductor derives

P type semiconductor is electrically neutral because total number of electron is equal to the total number of proton in P type semiconductor.

 

11.       Draw a ray diagram of an astronomical telescope in the normal adjustment position. State two drawback of this type of telescope.

 

11.       Astronomical Telescope: (In Normal Adjustment)

           

            (i)         Inverted image is formed

            (ii)        Fainter image is formed

 

12.       Calculate the distance of an object of height h from a concave mirror of focal length 10 cm, so as to obtain a real image of magnification 2.

 

12.       f = focal length = -10cm

            m = -2  = -v/u

             Þ        v = 2 u

            by mirror formula

                       

            Þ       

            Þ        cm

            Hence distance of object is 15 cm from mirror.

                 

 

13.       Draw the output wave form at X, using the given inputs A, B for the logic circuit shown below. Also identify the gate.

 

13.      

           

A

B

X¢

X

0

0

1

0

0

1

1

0

1

0

1

0

1

1

0

1

 

So, circuit performs AND operation.

for        t < t1     A = 0, B = 0                Hence X = 0

for        t1 to t2   A = 1, B = 0                Hence X = 0

for        t2 to t3   A = 1, B = 0                Hence X = 1

for        t3 to t4   A = 0, B = 1                Hence X = 0

for        t4 to t5   A = 0, B = 0                Hence X = 0

for        t5 to t6   A = 1, B = 0                Hence X = 0

for        t > t6     A = 0, B = 1                Hence X = 0

 

14.       A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m. What is the maximum distance between them, for satisfactory communication in the LOS mode? (Radius of earth = 6400 km)

 

14.       dm = Maximum distance between them LOS mode

                        =

                        = 46.51 km.

 

 

15.       Derive an expression for the potential energy of an electric dipole of the dipole moment  in an electric field 

15.       We know that

            = Torque   =

     *  = PE sin  q

      dW = work done to rotate it by an angle dq = clockwise)

      = = t (dq) × cos q (-ve sign is used q decreasing)

      dw = PE sinq dq

      Integrate this

      W = PE cos q                          (1)

As we know that the negative of work done by conservative force is equal to change in potential energy.

D U = -W = -PEcosq

or D U =   

 

 

16.       Define magnetic susceptibility of a material. Name two elements, one having positive susceptibility and the other having negative susceptibility.  What does negative susceptibility signify?

 

16.       The contribution to the total magnetic field inside the sample into two parts one due to external factors such as the current in the solenoid. This is represented by H. The other due to the specific nature of the magnetic material namely M. The latter quantity can be influenced by external factors. This factor is known on magnetic susceptibility.

                        M = XH

                        X ® magnetic susceptibility

            Positive value of X ® for chromium

            Negative value of X for - copper

            Negative susceptibility has lesser affinity for magnetic field. Those substance cannot be magnetized.

 

17.       The oscillating magnetic field in a plane electromagnetic wave is given by

           

            (i)   Calculate the wavelength of the electromagnetic wave.

            (ii)  Write down the expression for the oscillating electric field.

 

17.       By = (8 ´ 10-6) sin[2 ´ 1011 t + 300 p x]T

            Since B = B0

            On comparing

                        B0 = 8 ´ 10-6

                        w = 2 ´ 1011

                       

            \         m

            Since,  Þ E0 = B0 ´ C

                        = 8 ´ 10-6 ´ 3 ´ 108 = 24 ´ 102.

            Since direction of propagation of wave is along negative x-axis which is along

                        E2 = 24 ´ 102 sin[2 ´ 1011t + 300px]

 

18.       Prove that an ideal inductor does not dissipate power in an a.c. circuit.

OR

            Derive an expression for the self-inductance of a long air-cored solenoid of length l and number of turns N.

 

18.       Since in inductive circuit (when only inductor coil is used the direction of instantaneous current is perpendicular to  instantaneous alternating voltage.

                        e = eo sinwt

                        i =  -   Þ

            Average power in one complete cycle (P) = erms ´ irms ´ cosf

            which is zero as f = p/2.

OR

            Since magnetic flux associated to a coil is given by

                        f = Li where L is coefficient of self inductance

            Magnetic field induction

                        B = moni                       (1)

                        = m0 ´

            There are N number of turns, magnetic flux associated

                        f = (NA) ´ B

                        = (NA)mo    (2)

            on comparing we get coefficient of self inductance

                        L =

 

19.       Prove that the current density of a metallic conductor is directly proportional to the drift speed of electrons.

OR

            Define conductivity of a conductor. Explain the variation of conductivity with temperature in (a) good conductors (b) ionic conductors.

 

19.  Let A = area of cross –  

             section of the wire

       n = electron density, i.e.,

             number of free

            electrons per unit

           volume

     e= charge on each electron

    vd = drift velocity of free

           electron

 

 

In one second, all those free electrons within a distance vd to the right of cross –section at P (i.e., in a volume Avd) will flow through the cross-section at P as shown in figure. This volume contains n Avd electrons  and hence, a charge          (n A vd)e. Therefore, a charge of n e A vd per second passes the cross section at P.

            \         I = n e A vd

                        I/A = n e vd

                        J = n e vd

OR

            The conductivity of a material is its ability to conduct electric current. It is a measure of the ease with which the current flows through a conductor.

Electrical conductivity is defined as the reciprocal of resistivity.

 

(a)        Variation of resistivity of metal with temperature

       

 

      Resistivity is inversely proportional to

      relaxation time. When the

      temperature of a conductor is

      increased, the relaxation time is

      decreased on account of increased  

      atomic vibrations. Thus, resistivity

      increases with increase of

      temperature.

(b)        Dependence of conductivity of ionic conductor with temperature

            Conductivity of ionic conductor increases with increase in temperature. On increasing temperature the dissociation of ionic conductor increases as a result more number of ions will be produced.

 

20.     A potentiometer wire of

          length 1m is connected to

          a driver cell of emf 3V as

          shown in the figure. When

         a cell of 1.5 V emf is used

         in the secondary circuit, the

         balance point is found to be

        60 cm. On replacing this

        cell and using a cell of

        unknown emf, the balance

        point shifts to 80 cm.

        

            (i)   Calculate unknown emf of the cell.

            (ii)  Explain with reason, whether the circuit works, if the driver cell  is replaced with a cell of emf 1V.

            (iii) Does the high resistance R, used in the secondary circuit affect the balance point? Justify your answer.

20.       (i)        

                        E2 =  = 2V

            (ii)        The balance point will not be obtained on the potentiometer wire if fall of potential along the potentiometer wire is less than the emf of the cell to be measured.

                        So if we replace the drive cell by cell of 1V then this circuit will not work.

            (iii)       Under balanced condition no current flows through galvanometer wire so high resistance R does not affect the balance point.

 

 

21.       An  electromagnetic wave of wavelength l is incident on a photosensitive surface of negligible work function. If the photo-electrons emitted from this surface have the de –Broglie wavelength l1, prove that .

21.       Energy of incident photon = Kinetic Energy of emitted photoelectron

            (As work function is negligible)

                                                    (1)

multiple and divide by mass on right side of equation (1)                                   

                        mv = P =                            (2)

            Multiply and divide equation (1) by mass m and then substitute (mv)2 =  from equation (2)

                       

 

 

22.       The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength 102.7 nm.

22.                  

                        DE =  eV

                        DE = |EK - EM| = |-13.6 - (-1.50)|

                              = 12.1 eV

            Transition shown by arrow D corresponds to emission of l = 102.7 nm.           

 

 

23.       Draw a plot of the variation of amplitude versus w for an amplitude modulated wave. Define modulation index. State its importance for effective amplitude modulation.

 

23.

            Modulation index = amplitude of modulating signal / amplitude of carrier wave

            This modulation index is kept £ 1 to avoid distortion.

 

24.       How is a wave front defined? Using Huygen’s construction draw a figure showing the propagation of a plane wave reflecting at the interface of the two media. Sho