## Kerala Plus Two Physics Model Question Paper 5

**Time: 2 Hours**

**Cool off time : 15 Minutes**

**General Instructions to candidates:**

- There is a ‘cool off time’ of 15 minutes in addition to the writing time of 2 hrs.
- Your are not allowed to write your answers nor to discuss anything with others during the ‘cool off time’.
- Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
- Read questions carefully before you answering.
- All questions are compulsory and only internal choice is allowed.
- When you select a question, all the sub-questions must be answered from the same question itself.
- Calculations, figures and graphs should be shown in the answer sheet itself.
- Malayalam version of the questions is also provided.
- Give equations wherever necessary.
- Electronic devices except non programmable calculators are not allowed in the Examination Hall.

Speed of light, c = 3 x 10^{8}m/s

Mass of proton, m_{p} = 1.6726 x 10^{-27} kg

Mass of neutron, mn = 1.6749 x 10^{-27} kg

Planck’s constant, h = 6.626 x 10^{-34} Js

1eV=1.6 x 10^{-19 }J

Questions 1-7 carry 1 score each. Answer any six questions.

Question 1.

Write the expression for intensity of electric field near to the surface of a charged conductor with uniform charge density σ.

Question 2.

The unit of electrical resistivity is…………

Question 3.

E.m.f can be induced in a coil placed in an external magnetic field by:

a. Changing the intensity of magnetic field

b. Changing the area of coil

c. Changing the orientation of the coil

d. All of the above

Question 4.

Write the energy and momentum associated with a moving photon.

Question 5.

The value of relative permeability of a dia magnetic material is;

Question 6.

The electric field amplitude of an electromagnetic wave is 15V/m. Find the magnetic field amplitude of the wave.

Question 7.

A convex lens is placed in a medium having refractive index greater than that of the lens. The lens now behaves as;

a. Converging lens

b. Diverging lens

c. Plane glass plate

d. None of the above

Questions 8 to 15 carry 2 score each. Answer any 7 questions

Question 8.

a. ‘Electrostatic field is always normal to the surface of a charged conductor’. Justify the statement.

b. The value of electric potential at the surface of a charged conductor is 10 V. Find the value of intensity of electric field and potential at a point interior to it

Question 9.

A galvanometer with a coil of resistance 12 Ω shows a lull scale deflection for a current of 2.5 mA. How can it be converted into an ammeter of range 7.5 A?

Question 10.

The curves shown in figure are drawn for different magnetic materials. Among the three curves, name the curve that

a. Represent the material usually used for making permanent magnets.

b. Represent the material usually used for making electromagnets.

Question 11.

A capacitor C, a variable resistance R and a bulb B are connected in series to a.c mains in the circuit as shown. The bulb glows with some brightness. How the glow of the bulb change if.

a. A dielectric slab is introduced between the plates of the capacitor

b. The resistance R is increased keeping the same capacitance

Question 12.

James Clerk Maxwell modified Ampere’s circuital theorem by introducing the concept of displacement current.

a. What do you mean by displacement current?

b. Write down the equation for displacement current.

Question 13.

An object AB is kept in front of a concave mirror as shown in figure.

a. Complete the ray diagram showing the image formation of object

b. How will the position and intensity of image be affected if the lower half of the mirror’s reflecting surface is painted black?

Question 14.

Assuming that the two diodes D1 and D2 used in the electric circuit as shown in figure are ideal. Find out the value of current flowing through 2.5 Ω resistor.

Question 15.

a. Mention the function of the following used in the communication system

i. Transducer

ii. Transmitter

b. Figure shows the block diagram of a AM transmitter. Identify the boxes X and Y.

Questions 16 to 22 carry 3 scores each. Answer any 6 questions.

Question 16.

Three capacitors of capacitances 2µF, 3µF and 4µF are connected in series.

a. Find the equivalent capacitance of the combination.

b. The plates of a parallel plate capacitor have an area 20 cm² each are separated by a distance of 2.5 mm. The capacitor is charged by connecting it to a 400V supply. How much electrostatic energy is stored in the capacitor?

Question 17.

A circuit using potentiometer and a battery of. negligible internal resistance is set up as shown to develop a constant potential gradient along the wire PQ. Two cells of e.m.f s E1 and E2 are connected in series as in figure in combination 1 and 2. The balance points are obtained respectively at 400 cm and 240 cm from point P. Find

Question 18.

A conducting rod PQ of length ‘ l ’ connected to a resistance ‘R’ is moved at a uniform speed ‘ V’, normal to a uniform magnetic field ‘B’

a. Deduce the expression for e.m.f induced in the conductor

b. Find the magnitude and direction of current through the conductor

Question 19.

In tuner circuits, we use the phenomenon of resonance.

a. Write the condition of resonance in series LCR circuit

b. A series LCR circuit uses L = 0. 1 H,C = 10µF and R = 100Ω. Find the value of frequency at which the amplitude of current is maximum

Question 20.

The focal length of a lens has dependence on its radii of curvatures and refractive index. Derive Lens maker’s formula

Question 21.

a. Write the expression for the de Broglie wavelength associated with a charged particle having charge ‘q’ and mass ‘m’, when it is accelerated by a potential of ‘V’ volts.

b. A proton and an electron have same kinetic energy. Which one has greater value of de Broglie wavelength and why?

Question 22.

Find the binding energy per nucleon of _{20}^{40}Ca nucleus. Given m _{20}^{40}Ca = 39.962589u.

m_{p} = 1.00783u, m_{n} = 1.00867u

Take 1 amu = 931 MeV/c^{2}

Questions from 23-26 carry 4 score. Answer any 3 questions.

Question 23.

Gauss’s theorem is useful for finding the intensity of electric field.

a. Write the Gauss’s law in its mathematical form

b. Using the law, prove that intensity of electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it

Question 24.

a. Express Ohm’s law in terms of current density, electrical resistivity and intensity of electric field

b. Explain the variation of resistance of a semiconductor with temperature. Also draw the graph showing the variation of resistivity of silicon with temperature

Question 25.

The relation between magnetic field and current is given by Biot-Savart’s law.

a. Write the expression for the magnetic field at point along the axis of a circular loop of radius ‘R’ carrying a current ‘I’.

b. From the above expression. Find the value of magnetic field at the centre of the loop

c. Sketch the magnetic field lines for current carrying circular loop

Question 26.

a. Identify the diode in the circuit and write the use of the resistance R_{s}

b. Explain how the diode helps as to stabilize the output voltage of the circuit

c. Name the type of biasing used in this diode

Questions 27 to 29 carry 5 scores. Answer any 27 – 29 carry 5 score. Answer any 2 questions

Question 27.

In the figure, PQ is the incident ray on the equilateral glass prism ABC.

a. Complete the ray diagram showing the passage of light and mark angle of deviation.

b. Derive an expression for the refractive index of the material of the prism

Question 28.

According to Christian Huygens wave theory, light emanating from a source as wave fronts.

a. What is the shape of wave front emerging form a linear source?

b. Derive the mathematical expression for the bandwidth of interference bands obtained in young’s double slit experiment with the help of suitable diagram

Question 29.

a. The radius of n^{th} stationary orbit of hydrogen atoms is :

Using Bohr postulates, obtain an expression for the energy of electron in the stationary states of H-atom

b. Draw the energy level diagram showing how the spectral lines corresponding to Balmer series occur due to transition between the energy levels

**Answers**

Answer 1.

\(E=\frac { \sigma }{ { \varepsilon }_{ 0 } } \)

Answer 2.

Ωm

Answer 3.

(d)All the above

Answer 4.

E = hυ = bc/λ

\(P=\frac { h }{ \lambda } =\frac { h\upsilon }{ c } \)

Answer 5.

µ_{r} < 1 or µ_{r} = 0

Answer 6.

Answer 7.

b. Diverging lens

Answer 8.

a. If E is not normal, there is a component a long the tangent to the surface. Then free charge on the surface experience force and will move. But E should have no tangential component in static situation.

OR

V is constant on the surface, therefore E should be normal.

b. E = 0, V = 10V

Answer 9.

G = 12V, Ig = 2.5×10^{-3} A

I = 7.5 A

Putting the low resistance S in parallel with the galvanometer

Answer 10.

a. A

b. C

Answer 11.

a. E_{r} introduced, capacitance increases i.e,.\(\frac { 1 }{ c\omega } \) will decrease ∴ I_{0} will be increase so the brightness will be increased

b. R ↑, I_{0 }↓ brightness ↓

resistance cause decrease in I_{0} ∴ bright ness will be decreased

Answer 12.

a. Displacement current is current due to time varying electric flax

Answer 13.

b.No change in position intensity halved/reduced

Answer 14.

D_{2} on reverse biasing so it does not conduct

D_{1} on forward biasing so it conduct

R = 3 + 2.5 = 5.5

V = 10V

I = \(\frac { V }{ R }\) = \(\frac { 10 }{ 5.5 }\) = l.82A

Answer 15.

a. i. Convert energy from one form to an other.

ii. Convert message signal to modulated signal for transmission.

b. X → modulater

Y → Power amplifier

Answer 16.

Answer 17.

E α l

Answer 18.

a. The magnetic flux linked with the rectangular loop PQRS is φ = BA = Blx

According to Faraday’s law, induced emf is

Answer 19.

a. V_{L }= V_{C}

X_{L} = X_{C}

Answer 20.

Answer 21.

Answer 22.

BE = E_{b} = ∆mc²

= (Zmp + (A-Z) Mn – M) c²

= (20 x 1.00783 + 20 x 1.00867 – 39.962589) x

Answer 23.

Answer 24.

a. I = ne A V_{d}……….(1)

Answer 25.

Answer 26.

a. Zener diode

Any change in input voltage results in change in voltage drop across Rs. without any change in voltage across zener diode.

b. When V_{i} increases, main current increases, I_{z} increases with no change in load current I_{L}. So that V_{0} = V_{z} = I_{L} R_{L}. When V_{i} decreases, I_{z} decreases with no change in I_{L}.

c. Reverse biasing

Answer 27.

Answer 28.

a. Cylinder

b. S1 and S2 are two narrow slits separated by a distance “d”. They are illuminated by a monochromatic source of wavelength λ . A screen is placed at a distance of D from the slits as shown in the figure

Light waves from S1 and S2 reach the point P. The path difference between these two waves is S2N.

Answer 29.

a. For a hydrogen atom, gives the expression to determine the energies of different energy states. But then this equation requires the radius r of the electron orbit. To calculate r, Bohr’s second postulate about the angular momentum of the electron-the quantization condition is used. The angular momentum L is given by

L = mvr

Bohr’s second postulate of quantization says that the allowed values of angular momentum are integral multiples of h/2π

where n is an integer, r_{n} is the radius of nth possible orbit and u_{n} is the speed of moving electron in the nth orbit. The

allowed orbits are numbered 1,2,3………

according to the values of n, which is called the principal quantum number of the orbit.

From the relation between u_{n} and r_{n} is