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______________________________________________________TutorBreeze.com Answers to 2008 CBSE Physics Paper I have answered the questions and taken care that there are no errors. In case of any errors that might have crept in please write to me at [email protected]. In case of any confusion or if you would like to discuss any answers you can leave a question in FREE homework help forum at http://www.TutorBreeze.com. I have written the answers to set 3, there are minor variations in questions in other sets. In case there are any particular questions for which you wish to know the answers please write to me or post them on the website. Physics (Theory)− −2008 Code No. 55/3 Time Allowed: 3 hours] 1. [Maximum Marks: 70 What is the nuclear radius of 125Te, if that of 27Al is 3.6 fermi? R = R0 A1/3 Ans. R Al AAl1/3 271/3 = = ( ) RTe ATe1/3 561/3 1251/3 RTe = ( ) × R Al 271/3 2. A diverging lens of focal length ‘F’ is out into two identical parts each forming a plano-concave lens, what is the focal length of each part? 1 n2 2 = ( − 1)(− ) f n1 R n2 1 1 = ( − 1)( − ) R f ' n1 2f = f ' 3. What is the geometrical shape of the wavefront when a plane wave passes through a convex lens. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com 4. What is the stopping potential applied to photocell, if the maximum kinetic energy of electrons emitted is 5 eV. KE = eV0 5eV = eV0 V0 = 5volts 5. Draw an equipotential surface for a uniform electric field. 7. Identify the part of the electromagnetic spectrum to which the following wavelengths belong:(i) 10-1m (ii) 10-12 m 1) 10-1 m corresponds to microwaves ii) gamma rays _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com 8. When current in a coil changes with time, how is the back emf induced in the coil related to it? ε =− 9. dφ dt State the law of radioactive decay. If N0 is the number of radioactive nuclei in the sample at some initial time, t0, find out the relation to determine the number N present at a subsequent time. Draw a plot of N as a function of time. OR Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei.Explain the energy release in the process of nuclear fission from the above plot. Write a typical nuclear reaction in which a large amount of energy is released in the process of nuclear fission. The law of radioactive decay states that the rate of decay is proportional to the number of dN nuclei present. ∝N dt dN ∝N dt dN = −λ N dt dN = −λdt N Integrating N t ln N = −λ (t − t 0 ) N0 dN ∫N N = −t∫ λdt 0 0 N = N 0e − λ (t −t0 ) _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com OR Elements with high mass number have low values of binding energy. This implies that they are less stable. By undergoing nuclear fission they can have lower values of A and hence higher values of binding energy which means they are more stable. 235 89 1 U 92 + n 10 → Ba 144 56 + Kr36 + 3n 0 10.Why do we need carrier waves of very high frequency in the modulation of signals? A carrier wave of peak voltage 20V is used to transmit a message signal. What should be the peak voltage of the modulating signal, in order to have a modulation index of 80%. As size of antenna required is comparable to wavelength of waves, high frequency waves will require smaller antenna. High frequencies are transmitted better as power radiated increases with increasing frequency. Modulation index= message or modulating signal amplitude carrier amplitude 80 x = 100 20 _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com 11. Using Gauss’s law derive an expression for the electric field intensity at any point near a uniformly charged thin wire of charge/length λ C/m. Derivation is given in NCERT text book. Choose a cylinder as a gaussian surface and find flux through it, equate it to charge enclosed. 12. The following graph shows the variation of terminal potential difference V, across, combination of three cells, in series to a resistor, versus the current. (i) calculate the emf of each cell. (ii) For what current i, will the power dissipation of the circuit be maximum? The internal resistance of each cell is r, then the 3 cells placed in series have a total resistance of 3r. V = E − ir , for current equal to zero, V = E. So emf of each cell is 2V. Power dissipation is maximum for R= 3r, i = 3E 3E E = = R + 3r 3r + 3r 2r We need to find r. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com V = E − ir 3 = 6 − 1(3r ) From graph we saw that for V=3, i = 1A and E is fixed 3r = 3 r = 1Ω Power dissipation maximum for i = E 2 = = 1A 2r 2 × 1 13. What is meant by the transverse nature of electromagnetic waves? Draw a diagram showing the propagation of an electromagnetic wave along the xdirection, indicating clearly the directions of the oscillating electric and magnetic fields associated with is Transverse nature of em waves means that the electric field and magnetic field are perpendicular to each other and to the direction of propagation of the waves. The vector product E × B point in the direction of propogation. 14. In the figure given below, light rays of blue, green, red – wavelengths are incident on an isosceles right-angled prism. Explain with reason, which ray of light will be transmitted through the face AC. The refractive index of the prism for red, green, blue light are 1.39, 1.424, 1.476 respectively. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com Angle of incidence is 450. Critical angles corresponding to these 3 values of refractive index is sin i 1 = sin 90 1.39 critical angle for 1.39 is 46 deg rees critical angle for 1.476 is42 deg rees As angle of incidence is greater than critical angle, the light will emerge through AC. This is true for red. 15. Two wires X, Y have the same resistivity, but their cross sectional areas are in the ratio 2 : 3 and lengths in the ratio 1 : 2 . They are first connected in series and then in parallel to a d.c. source. Find out the ratio of the drift speeds of the electrons in the two wires for the two cases. R1 = ρ l l1 ; R2 = ρ 2 A1 A2 A A R1 l l 1 2 1 = 1 × 2 = 1× 2 = × = R2 A1 l 2 l 2 A1 2 3 3 _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com i1 = V V = R1 + R2 4x i2 = V V 4 = = V R1R2 3x / 4 3x R1 + R2 i1 V 3x 3 = × = i2 4x 4V 16 i1 = neA1v1 i2 = neA2v 2 i1 Av 2 v1 = 1 1 = i2 A2v 2 3 v 2 3 2 v1 = 16 3 v 2 v1 9 = v 2 32 16. Define the term: magnetic dipole moment of a current loop. Write the expression for the magnetic moment when an electron revolves at a speed ‘v’ around an orbit of radius ‘ r’ in hydrogen atom. Magnetic moment m = IA where I is the current and A is the area of the loop. Time period and hence frequency of electrons is 2π r v v f = 2π r T = v ) 2π r We need to find out current, or charge/time = ch arg e / time = 1sec ond e( m = [e ( 17. v evr )][π r 2 ] = Am2 2π r 2 In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? Draw a plot of the intensity distribution. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com Central diffraction band = 2λ a If ‘a’ is doubled, central band = 2λ λ = so size reduces to half 2a a Intensity increases 4 times. 18. A jet plane is travelling west at 450 ms-1. If the horizontal component of earths magnetic field at that place is 4 × 10-4 T and the angle of dip is 300, find the emf induced between the ends of wings having a span of 30 m. Induced emf = Blv Horizontal component of earth's field = Bcos300 = 4 × 10−4 T B= 4 × 10−4 T cos300 4 × 10 −4 T sin 30 cos300 T) (tan 300 )(30m )(450m / s ) Vertical component of earth's field = Bsin300 = Induced emf = Bcosθ lv = (4 × 10 −4 19. What does the term LOS communication mean ? Name the types of waves that are used for this communication. With the help of a suitable figure, of communication systems that use space wave mode propagation. Line of sight communication. It refers to direct reception of waves. The space waves travel in a straight line from the transmitting antenna to the receiving antenna. Space waves are used for LOS. Television , microwaves and satellite communication use space waves. Diagram given in NCERT text book. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com 20. Draw a plot showing the variation of power of a lens, with the wavelength of the incident light. A converging lens of refractive index 1.5 and of focal length 15 cm in air, has the same radii of curvature for both sides. If it is immersed in a liquid of refractive index 1.7, find the focal length of the lens in the liquid. n glass 1 1 1 =( − 1)( − ) f air nair R1 R 2 n glass 1 1 1 =( − 1)( − ) f liq nliq R1 R 2 Taking ratio of both equations n ( glass − 1) f liq n air = n f air ( glass − 1) nliq Substitute and find the answer 21. Draw V-I characteristics of a zener diode. Explain with the help of a circuit diagram how a zener diode can be used as a voltage regulator. OR With the help of a circuit diagram, explain the working principle of full wave rectifier. Draw the input and output waveforms. Diagram and waveforms are given in NCERT textbook . _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com Across the zener diode voltage remains constant even though the current through it changes. Example if the input voltage decreases, the current through the series resistor in the circuit decreases and through the zener diode also decreases. The voltage across the series resistor will decrease but the voltage across the zener diode will not change. Thus the zener diode acts as a voltage regulator. 22. A resistance R = 4Ω is connected to one of the gaps in a meter bridge, which uses a wire of length 1 m. An unknown resistance X > 4Ω is connected in the other gap as shown in the figure. The balance point is noticed at T from the positive end of the battery. On interchanging R and X, it is found that the balance point further shifts by 20 cm (away from end A) . Neglecting the end correction, calculate the value of unknown resistance X used. 4 l = X (100 − l ) X l + 20 = 4 100 − (l + 20) Mutiple the two equations and find l OR Show that Bohr’s second postulate, the electron revolves around the nucleus only in certain fixed orbits without radiating energy can be explained on the basis of the Broglie hypothesis of wave nature of electron. According to Bohr’s second postulate the electrons revolves in orbits for which the h angular momentum is an integral multiple of . The angular momentum is 2π nh quantised and L = . 2π _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com For electron in an orbit, its circumference contains an integral number of deBroglie wavelengths. 2π r = nl = n ( h ); l is the deBroglie wavelength of electron mv nh 2π nh L= 2π mvr = 24. If a particle of charge q is moving with velocity v along the x-axis and the magnetic field B is acting along the y-axis, use the expression the direction of the force F acting on it. to find A beam of proton passes undeflected with a horizontal velocity v, through a region of electric and magnetic fields, mutually perpendicular to each other and normal to the direction of the beam. If the magnitudes of the electric and fields are 50 kV/m, 100 mT respectively, calculate (i) velocity v of the beam (ii) force with which it strikes a target on the screen, if the proton beam current is equal to 0.80 mA.. v = viˆ; B = Bjˆ F = qvBkˆ As proton passes undeflected, qE=qvB v= E 50 × 1000 = m /s B 100 × 10 −3 Force is equal to dp/dt. This is force exerted by 1 proton. F = dp d (mv ) = dt dt _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com Using current we can find the number of protons hitting the screen. I=q/t Q = (0.80 x10-3A)(1 second) = 0.80 x10-3C Number of protons hitting the screen = Q/charge of a proton Total force = (mvQ)/ charge of a proton. Substitute all values, mass of proton, vel of proton(solved above), charge of proton, and given in question. 25. Distinguish between isotopes and isobars. Give one example for each of the species. A radioactive isotope has a half-life of 5 years. How long will it take the activity to reduce to 3.125%? Isotopes have same atomic no. Isobars have same mass no. Isotopes of hydrogen are deuteron and triton. Isobars are argon and calcium. 3.125% = 3.125 1 = 0.03125 = ( )5 100 2 5 half lifes will be required. Hence time required is 5x(half life or isotope) = 25 years 26. Distinguish between paramagnetic and diamagnetic substances. A magnetizing field of 1500 A/m produces a flux of 2.4 × 10-5 weber in a bar of iron of cross sectional area 0.5 cm2. Calculate the permeability and susceptibility of the iron bar used. Properties of para and dia given in book. H = 1500 A / m B = µH Φ = B .A; Φ 2.4 × 10 −5 Wb = = 0.48T A 0.5 × 10 −4 m 2 B 0.48 = = 0.00032 = 3.2 × 10 −4 µ= H 1500 B= _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com µr = 1 + χ Susceptibility µr = µ 3.2 × 10−4 = = 255 µ0 4π × 10−7 χ = 254 27. Two signals A, B as given below, are applied as input to (i) AND (ii) NOR and (iii) NAND gates. Draw the output wave – form in each case. Using the truth table for each of these gates combine the 2 inputs to get the output. 28. Draw a labeled ray diagram of a compound microscope and write an expression for its magnifying power. The focal lengths of the objective and eye-lens of a compound microscope are 2cm, 6.25 cm respectively. The distance between the lenses is 15 cm. (i) How far from the objective lens, will the object be kept, so as to obtain the final image at the near point of the eye ? (ii) Also calculate its magnifying power. OR Draw a labeled ray diagram of an astronomical telescope, in the normal adjustment position and write the expression for its magnifying power. An astronomical telescope uses an objective lens of focal length 15 m and eye-lens of focal length 1 cm. What is the angular magnification of the telescope? If this telescope is used to view Moon, what is the diameter of the image of Moon formed by the objective lens? (Diameter of Moon = 3.5 × 106 m and Radius of lunar orbit = 3.8 × 108 m) Ray diagrams can be checked from your NCERT textbook _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com i )For objective lens 1 f 0bjective = 1 1 − v u f = 2cm; u = u ; u and v are both unknown so first use eyepiece For eyepiece 1 = f eye 1 1 − v u f = 6.25cm ; u = u;v = −25cm 1 1 1 1 1 = − = − u v f −25 6.25 u = −5cm 1 f 0bjective = 1 1 − v u f = 2cm; u = ? cm;v = (15 − 5) = 10cm 1 1 1 = − 2 10 u u = −2.5cm ii ) f 0 = 2cm ; f e = 6.25cm ; L = 15cm; D = 25cm m= L D (1 + ) f0 fe Substitute values and calculate magnifying power. m= OR f 0 15cm = = 15 fe 1cm Diameter of moon 3.5 × 106 = = 0.92 × 10 −2 radius of Lunarorbit 3.8 × 108 Size of image = 15 × 0.92 × 10 −2 m 29. State the condition for resonance to occur in a series LCR a.c. circuit and derive an expression for the resonant frequency. Draw a plot showing the variation of the peak current (im) with frequency of the a.c. source used. Define the quality factor, Q of the circuit. Calculate the (i) impedance, (ii) wattless current of the given a.c. circuit. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com Draw a labeled circuit arrangement showing the windings of primary and secondary coil in a transformer. Explain the underlying principle and working of a step up transformer. Write any two major sources of energy loss in this device. How much current is drawn by the primary coil of a transformer that step down 220 V to 22 V to operate device with an impedance of 220 ohm? Ans:Refer to the book for the derivation: ωL = 1 ωC Re sonant frequency= im = Q= 1 LC V R + ( X L − X C )2 2 ωL R can also be given by Q = 1 ωCR _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com 40 = iX C 30 = iR i = 2A X c = 20ohms R = 15ohms Z = R 2 + X 2c = 152 + 202 2= Vrms Z Wattless component of voltage is across the reactive components , here the capacitor. XC R X sin θ = C Z V sin θ is the wattless component of voltage. tan θ = If the circuit has only inductive and capacitive components then the current is called wattless current. OR Refer to the book for description of transformer and losses in transformers. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com Vs N s i p = = V p N p is Vs = i s R ; 22 = is (220) is = 1 10 i 22 = p 1 220 10 1 ip = A = 0.01A 100 30. (a) Derive an expression for the energy stored in a parallel plate capacitor C, charged to a potential difference V. (b) Obtain the equivalent capacitance of the network given below. For a supply of 300 V, determine the charge and voltage across C4. Explain the principle on which Van-de-Graaff generator operates. Draw a labeled schematic sketch and write briefly its working. . A Va-de-Graaff type generator is capable of building up potential difference of 15× 10 V. The dielectric strength of the gas surrounding the electrode is 5 × 107V m-1. What is the minimum radius of the spherical shell required? 6 You can look up your NCERT book for the Van-de-Graaff generator and derivation of energy stored in a capacitor. _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com C2 and C3 are in series so their combination is 100pF. This is in parallel with C1. This combination is 300pF. This 300pF is in series with C4. So total is 120pF. Q = CV = 120 × 10 −12 × 300C = 36 × 10 −9C = 36nC This charge is present in C4. Voltage across C4 is V = Q 36 × 10 −9 = = 180V C 200 × 10 −12 OR _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com ______________________________________________________TutorBreeze.com V = Ed 15 × 106 = (5 × 107 )d d= 15 × 106 = 0.3m 5 × 107 _____________________________________________________________________ Online Tutoring in Physics, Mathematics please visit http://www.TutorBreeze.com