Board Paper of Class 12-Science 2015 Physics (SET 1) - Solutions

A proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds. VIEW SOLUTION

Show that the radius of the orbit in hydrogen atom varies as n², where n is the principal quantum number of the atom. VIEW SOLUTION

Distinguish between 'intrinsic' and 'extrinsic' semiconductors. VIEW SOLUTION

Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?

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Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge. VIEW SOLUTION

Name the parts of the electromagnetic spectrum which is
(a) suitable for radar systems used in aircraft navigation.
(b) used to treat muscular strain.
(c) used as a diagnostic tool in medicine.
Write in brief, how these waves can be produced. VIEW SOLUTION

(i) A giant refracting telescope has an objective lens of focal length 15 m. If an eye piece of focal length 1.0 cm is used, what is the angular magnification of the telescope ?

(ii) 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 3.48 × 10⁶ m and the radius of lunar orbit is 3.8 × 10⁸ m. VIEW SOLUTION

Write Einstein's photoelectric equation and mention which important features in photoelectric effect can be explained with the help of this equation.

The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes from λ₁ to λ₂. Derive the expressions for the threshold wavelength λ₀ and work function for the metal surface. VIEW SOLUTION

In the study of Geiger-Marsdon experiment on scattering of α particles by a thin foil of gold, draw the trajectory of α-particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study.

From the relation R = R₀ A^1/3, where R₀ is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.
 
Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction :

${}_1{}^2\mathrm{H} + {}_1{}^3\mathrm{H} \underset{ }{\to } {}_2{}^4\mathrm{He} + \mathrm{n}$

Using the data :

$$\begin{gathered} \mathrm{m}\left({}_1{}^2\mathrm{H}\right) = 2.014102 \mathrm{u} \\ \mathrm{m}\left({}_1{}^3\mathrm{H}\right) = 3.016049 \mathrm{u} \\ \mathrm{m}\left({}_2{}^4\mathrm{He}\right) = 4.002603 \mathrm{u} \end{gathered}$$

m_n = 1.008665 u

1u = 931.5 MeV/c² VIEW SOLUTION

Draw a block diagram of a detector for AM signal and show, using necessary processes and the waveforms, how the original message signal is detected from the input AM wave. VIEW SOLUTION

A cell of emf 'E' and internal resistance 'r' is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.

It is found that when R = 4 Ω, the current is 1 A and when R is increased to 9 Ω, the current reduces to 0.5 A. Find the values of the emf E and internal resistance r. VIEW SOLUTION

Two capacitors of unknown capacitances C₁ and C₂ are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C₁ and C₂. Also calculate the charge on each capacitor in parallel combination. VIEW SOLUTION

State the principle of working of a galvanometer.

A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting a resistance R₁ in series with the coil. If a resistance R₂ is connected in series with it, then it can measures upto V/2 volts. Find the resistance, in terms of R₁ and R₂, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the galvanometer in terms of R₁ and R₂. VIEW SOLUTION

With what considerations in view, a photodiode is fabricated? State its working with the help of a suitable diagram.

Even though the current in the forward bias is known to be more than in the reverse bias, yet the photodiode works in reverse bias. What is the reason? VIEW SOLUTION

Draw a circuit diagram of a transistor amplifier in CE configuration.

Define the terms : (i) Input resistance and (ii) Current amplification factor. How are these determined using typical input and output characteristics? VIEW SOLUTION

Answer the following questions :

(a) In a double slit experiment using light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.

(b) Light of wavelength 5000 Å propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected? VIEW SOLUTION

An inductor L of inductance X_L is connected in series with a bulb B and an ac source. How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of reactance X_C = X_L is inserted in series in the circuit. Justify your answer in each case. VIEW SOLUTION

A group of students while coming from the school noticed a box marked "Danger H.T. 2200 V" at a substation in the main street. They did not understand the utility of a such a high voltage, while they argued, the supply was only 220 V. They asked their teacher this question the next day. The teacher thought it to be an important question and therefore explained to the whole class.

Answer the following questions:
(i) What device is used to bring the high voltage down to low voltage of a.c. current and what is the principle of its working ?
(ii) Is it possible to use this device for bringing down the high dc voltage to the low voltage? Explain
(iii) Write the values displayed by the students and the teacher. VIEW SOLUTION

(a) State Ampere's circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius 'r', having 'n' turns per unit length and carrying a steady current I.

(b) An observer to the left of a solenoid of N turns each of cross section area 'A' observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m = NIA.


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(a) Using Huygens's construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.

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

(c) Explain why the maxima at $\theta =\left(n+\frac{1}{2}\right) \frac{\lambda }{a}$ become weaker and weaker with increasing n.

OR

(a) A point object 'O' is kept in a medium of refractive index n₁ in front of a convex spherical surface of radius of curvature R which separates the second medium of refractive index n₂ from the first one, as shown in the figure.

Draw the ray diagram showing the image formation and deduce the relationship between the object distance and the image distance in terms of n₁, n₂ and R.

(b) When the image formed above acts as a virtual object for a concave spherical surface separatig the medium n₂ from n₁ (n₂ > n₁), draw this ray diagram and write the similar (similar to (a)) relation. Hence obtain the expression for the lens maker's formula.

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(a) An electric dipole of dipole moment $\underset{p}{\to }$ consists of point charges +q and −q separated by a distance 2a apart. Deduce the expression for the electric field $\underset{E}{\to }$ due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment $\underset{p}{\to }$. Hence show that in the limit $x>>a, \overrightarrow{E}\to 2\overrightarrow{p}/(4\mathrm{\pi } {\mathrm{\epsilon }}_0{x}^3)$.

(b) Given the electric field in the region $\overrightarrow{E}=2x\hat{i}$, find the net electric flux through the cube and the charge enclosed by it.

(a) Explain, using suitable diagrams, the difference in the behaviour of a (i) conductor and (ii) dielectric in the presence of external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility.

(b) A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge $\frac{Q}{2}$ is placed at its centre C and an other charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric flux through the shell.
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