Board Paper of Class 12-Science 2016 Physics (SET 2) - Solutions

The wavelength λ of a photon and the de-Broglie wavelength of an electron have the same value. Show that energy of a photon in (2λmc/h) times the kinetic energy of electron; where m, c and h have their usual meaning. VIEW SOLUTION

Distinguish between polarized and unpolarized light. Does the intensity of polarized light emitted by a polaroid depend on its orientation? Explain briefly.
The vibration in a beam of polarized light make an angle of 60° with the axis of the polaroid sheet. What percentage of light is transmitted through the sheet? VIEW SOLUTION

A metal rod of square cross-sectional area A having length l has current I flowing through it when a potential difference of V volt is applied across its ends (figure I). Now the rod is cut parallel to its length into two identical pieces and joined as shown in figure II. What potential difference must be maintained across the length of 2l. so that the current in the rod is still I?

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(i) State Bohr postulate of hydrogen atom that gives the relationship for the frequency of emitted photon in a transition.

(ii) An electron jumps from fourth to first orbit in an atom. How many maximum number of spectral lines can be emitted by the atom? To which series these lines correspond?
Use de-Broglie's hypothesis to write the relation for the n^th radius of Bohr orbit in terms of Bohr's quantization condition of orbital angular momentum. VIEW SOLUTION

A device X used in communication system can convert one form of energy into another. Name the device X. Explain the function of a repeater in a communication system. VIEW SOLUTION

Three rays (1, 2, 3) of different colours fall normally on one of the sides of an isosceles right angled prism as shown. The refractive index of prism for these rays is 1.39, 1.47 and 1.52 respectively. Find which of these rays get internally reflected and which get only refracted from AC. Trace the paths of rays. Justify your answer with the help of necessary calculations.

Describe an activity to show that the colours of white light splitted by a glass prism can be recombined to get white light by another identical glass prism. Also, draw a ray diagram to show the recombination of the spectrum of white light. VIEW SOLUTION

(i) Describe the working principle of a solar cell. Mention three basic processes involved in the generation of emf.

(ii) Why are Si and GaAs preferred materials for solar cells? VIEW SOLUTION

In the following arrangement of capacitors, the energy stored in the 6 µF capacitor is E. Find the value of the following :

(i) Energy stored in 12 µF capacitor.

(ii) Energy stored in 3 µF capacitor.

(iii) Total energy drawn from the battery.

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(i) Define 'activity' of a radioactive substance.

(ii) Two different radioactive elements with half lives T₁ and T₂ have N₁ and N₂ undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N₁ and N₂. VIEW SOLUTION

Plot a graph showing the variation of photoelectric current with intensity of light. The work function for the following metals is given:

Na: 2.75 eV and Mo : 4.175 eV.

Which of these will not give photoelectron emission from a radiation of wavelength 3300 $\stackrel{\circ }{\mathrm{A}}$ from a laser beam? What happens if the source of laser beam is brought closer?
 
Define the term "cut off frequency" in photoelectric emission. The threshod frequency of a metal is f. When the light of frequency 2f is incident on the metal plate, the maximum velocity of photo-electrons is v₁. When the frequency of the incident radiation is increased to 5f, the maximum velocity of phto-electrons is v₂. Find the ratio v₁ : v₂. VIEW SOLUTION

(a) Distinguish between point to point and broadcast modes of communication. Give an example of each.

(b) Explain the basic concept of mobile telephoning. VIEW SOLUTION

Two identical coils P and Q each of radius R are lying in perpendicular planes such that they have a common centre. Find the magnitude and direction of the magnetic field at the common centre of the two coils, if they carry currents equal to $I$ and $\sqrt{3}I$  respectively.

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(i) Define self-inductance. Write its SI units.

(ii) A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing? VIEW SOLUTION

(a) Define torque acting on a dipole of dipole moment $\overrightarrow{p}$ placed in a uniform electric field $\overrightarrow{\mathrm{E}}$. Express it in the vector from and point out the direction along which it acts.

(b) What happens if the field is non-uniform?

(c) What would happen if the external field $\overrightarrow{\mathrm{E}}$ is increasing (i) parallel to $\overrightarrow{p}$ and (ii) anti-parallel to $\overrightarrow{p}$? VIEW SOLUTION

(a) A point charge q moving with speed v enters a uniform magnetic field B that is acting into the plane of the paper as shown. What is the path followed by the charge q and in which plane does it move?

(b) How does the path followed by the charge get affected if its velocity has a component parallel to $\overrightarrow{B}$?

(c) If an electric field $\overrightarrow{E}$ is also applied such that the particle continues moving along the original straight line path, what should be the magnitude and direction of the electric field $\overrightarrow{E}$?

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(i) Which segment of electromagnetic waves has highest frequency? How are these waves produced? Give one use of these waves.

(ii) Which em waves lie near the high frequency end of visible part of em spectrum? Give its one use. In what way this component of light has harmful effects on humans? VIEW SOLUTION

In the following diagram, an object 'O' is placed 15 cm in front of a convex lens L₁ of focal length 20 cm and the final image is formed at I at a distance of 80 cm from the second lens L₂. Find the focal length of the lens L₂.

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Gautam went for a vacation to the village where his grandmother lived. His grandmother took him to watch 'nautanki' one evening. They noticed a blackbox connected to the mike lying nearby. Gautam's grandmother did not know what that box was. When she asked this question to Gautam, he explained to her that it was an amplifier.

(i) Which values were displayed by the grandmother? How can inculcation of these values in students be promoted?

(ii) What is the function of an amplifier?

(iii) Which basic electronic device is used in the amplifier? VIEW SOLUTION

A 2 µF capacitor, 100 Ω resistor and 8 H inductor are connected in series with an AC source.

(i) What should be the frequency of the source such that current drawn in the circuit is maximum? What is this frequency called?

(ii) If the peak value of e.m.f. of the source is 200 V, find the maximum current.

(iii) Draw a graph showing variation of amplitude of circuit current with changing frequency of applied voltage in a series LRC circuit for two different values of resistance R₁ and R₂ (R₁ > R₂).

(iv) Define the term 'Sharpness of Resonance'. Under what condition, does a circuit become more selective?
 
(i) With the help of a neat and labelled diagram, explain the principle and working of a moving coil galvanometer.

(ii) What is the function of uniform radial field and how is it produced?

(iii) Define current sensitivity of a galvanometer. How is current sensitivity increased? VIEW SOLUTION

(i) In the circuit diagram given below, AB is a uniform wire of resistance 15 Ω and length 1 m. It is connected to a cell E₁ of emf 2V and negligible internal resistance and a resistance R. The balance point with another cell E₂ of emf 75 mV is found at 30 cm from end A. Calculate the value of R.



(ii) Why is potentiometer preferred over a voltmeter for comparison of emf. of cells?

(iii) Draw a circuit diagram to determine internal resistance of a cell in the laboratory.
 
(i) Plot a graph showing variation of voltage vs the current drawn from the cell. How can one get information from this plot about the emf of the cell and its internal resistance?

(ii) Two cells of emf's E₁ and E₂ and internal resistance r₁ and r₂ are connected in parallel. Obtain the expression for the emf and internal resistance of a single equivalent cell that can replace this combination? VIEW SOLUTION

(i) State the essential conditions for diffraction of light.

(ii) Explain diffraction of light due to a narrow single slit and the formation of pattern of fringes on the screen.

(iii) Find the relation for width of central maximum in terms of wavelength 'λ', width of slit 'a', and separation between slit and screen 'D'.

(iv) If the width of the slit is made double the original width, how does it affect the size and intensity of the central band?
 
(i) Draw a labelled schematic ray diagram of astronomical telescope in normal adjustment.

(ii) Which two aberrations do objectives of refracting telescope suffer from? How are these overcome in reflecting telescope?

(iii) How does the resolving power of a telescope change on increasing the aperture of the objective lens? Justify your answer. VIEW SOLUTION