CBSE ANNUAL PAPER - 1999

PHYSICS

(SET-I)

Time allowed : 3 hours

Maximum Marks : 70

General Instructions :

(i) All questions are compulsory.

(ii) Marks for each question are indicated against it.

(iii) Question numbers 1 to 8 are very short - answer questions, carrying 1 mark each. These are to be answered in one or two sentences.

(iv) Questions numbers 9 to 18 are short - answer questions, carrying 2 marks each. Answer to these questions should be around 30 words each.

(v) Questions numbers 19 to 27 are also short - answer questions, each carrying 3 marks each. Answer to these questions should be around 50 words each.

(vi) Questions numbers 28 to 30 are long - answer questions, each carrying 5 marks. Answer to these questions should around 100 words each.

(vii) Use Log Tables, if necessary.

Draw an equipotential surface in a uniform electric field.

If a wire is stretched to double its original length without loss of mass, how will the resistivity of the wire be influenced?

Why do magnetic lines of force prefer to pass through iron than through air?

This is because magnetic permeability of iron is much higher than that of air.

What is the power factor of an LCR series circuit at resonance?

Why is the transmission of signals using ground waves restricted to frequencies upto 1500 KHz?

This is because the waves having frequency higher than 1500 KHz get largely absorbed during their propagation near the ground.

The polarizing angle of a medium is 60^o. What is the refractive index of the medium ?

How does the collector current change in a junction transistor, if the base region has larger width?

Two stars A and B have magnitudes -2 and + 4 respectively. Which star appears brighter ?

An electric flux of -6 X 103 Nm2/C passes normally through a spherical Gaussian surface of radius 10cm, due to a point charge placed at the centre.

1. What is the charge enclosed by the Gaussian surface?

2. (ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the surface ?

q = e0 Æ B = 8.85 x 10^-12 x (-6 x 10³) = -53.1 x 10^-9 C.

= -53.1 nC.

(ii) Since the charge enclosed is same in both coses, therefore, Æ B = -6 x 10³ Nm² C-1.

Three identical resistors, each of resistance R, when connected in series with a d.c. source, dissipate power X. If the resistors are connected in parallel to the same d.c. source, how much power will be dissipated ?

The equivalent resistance when in parallel is R/3.

Power dissipated = Vi = 3V²/R = 3 X 3 (V²/3R) = 9X [V²/3R= X]

Define mutual induction. State two factors on which the mutual inductance between a given pair of coils depends.

Whenever the current is one coil (Primary coil) changes, the magnetic flux linked with the second coil (Secondary coil) changes and an induced E.M.F. is set up in the Secondary coil. This phenomenon is called mutual induction. It depends on two factors :

(i) The number of turns in primary land secondary coil.

(ii) The material of iron core placed inside the coil. If the core is of soft iron, then value of M increases.

Light from a galaxy, having wavelength of 6000 A, is found to be shifted towards red by 50 A. Calculate the velocity of recession of the galaxy.

A converging lens has a focal length of 20 cm in air. It is made of materials of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, what will be its new focal length ?

or 1/20 = (1.6/1 - 1) (1/R₁ - 1/R₂) ......(1)

I/fw = (m_g /m _w -1) ( 1/R₁ - 1/R₂) ... ..(2)

Dividing (1) by (2), we get

f_w / 20 = 0.6 x 1.3 x 20 / 0.3 = 52 cm.

Draw a labelled ray diagram to show the image formation in an astronomical telescope for normal adjustment position. Write down the expression for its magnifying power.

Tube length fo + fe = 36

magnifying power = fo/fe = 8

Solving we get fe = 4 cm.

and fo = 32 cm.

The half-life of a radioactive sample is 30 seconds. Calculate (i) the decay constant, and (ii) time taken for the sample to decay to 3/4 th of its initial value.

(i) Disintegration constant l = 0.693/T_1/2 = 0.693/30 = 0.0231 s^-1.

(ii) By definition of half-life, 1/2 of the initial mass remains undisintegrated in 30 seconds. 1/4 of initial mass remains undisintegrated in next 30 seconds. so, 3/4 th of the initial mass disintegrates in 60 seconds.

When both the inputs of a NAND gate are connected together, it gets converted into a NOT gate. Both the inputs A and B will become low or high simultaneously.

For A = B, the truth table of NAND gate reduces into that of NOT gate. Figure shows the logic circuit for the realisation of a NOT gate from a NAND gate.

What is an ideal diode? Draw the output waveform across R, for the input waveform given below :

An ideal diode is one which offers zero resistance during forward biasing and infinite resistance during reverse biasing. The output wave form across R will be as shown in the figure.

Briefly describe, with the help of a diagram, the method to determine the distance of an inferior planet from the earth.

The angle formed at the earth between the earth-planet direction and the earth - sun direction is called the planet's alongation. This angle is denoted by symbol

Î, the planet appears farthest - from the sun. In this position the angle subtended by the sun and the earth at the planet is 90⁰.

r_ps / r_es = sin e

Distance of the planet from the sun is

r_ps = sin e. r_es = sin e . AU

whese r_es = IAU = average earth - sun distance.

Explain, with the help of a circuit diagram, the use of potentiometer for determination of internal resistance of a primary cell. Derive the necessary mathematical expression.

The resistance offered by electrolyte inside the cell circuit is called internal resistance of cell.

Let there be a cell of emf E, internal resistance r, used to draw current in a circuit of resistance r. then

I = E/R+r

IR + Ir = E

IR + IR = E

Ir = E-V

Or r = E-V/I

Or r = (E-V)R/V .....(i)

EMF is maximum P.D. obtainable by a cell when it is in open circuit.

The internal resistance of a primary cell can be determined by potentiometer. The circuit is shown below :

First insert infinite resistance from Resistance box and find null diflection length (l1). Since the cell is in open circuit.

E = Kl₁ .............. (ii)

Now insert a know resistance R from Resistance box and again find null deflection lelngth (l2). Since now the cell is in closed circuit so.

V = Kl₂ ............(iii)

By (i) r = (l₁-l₂) /R/l₂

Thus internal resistance of cell is determined.

Given circuit is equivalent to Wheat stone bridge shown in the figure.

The bridge is balanced. The 10 W resistance is not effective. We have (2W + 4W) and ( 1W+ 2W) resistances in parallel.

\ 1/R = 1/6 + 1/3 = 1/2

or R = 2 W

State Faraday's law of electrolysis. Write down the relation connecting chemical equivalent and electro-chemical equivalent.

An electron is moving at 10⁶ m/s in a direction parallel to a current of 5 A, flowing through an infinitively long straight wire, separated by a perpendicular distance of 10 cm in air. Calculate the magnitude of the force experienced by the electron.

F = qvB SIN 90⁰ = 1.6 x 10^-19 x 10⁶ x 10^-5 x 1

= 1.6 x 10^-18 N.

A bar magnet, held horizontally, is set into angular oscillations in Earth's magnetic field. It has time periods T 1 and T2 at two places, where the angles of dip are q1 and q2 respectively. Deduce an expression for the ratio of the resultant magnetic fields at the two places.

T₁ = 2p (1/mH₁)^1/2 = 2p ( 1/mB₁ cosq₁) ^1/2

At second place,

T₂ = 2p (I/mH₂)^1/2 = 2p (1/mB2 cosq₂)^1/2

^T₁ ^/T₂ ^{= (B2} cosq₂^{/ B}₁ cos cos q₁^{) or}

^{B1 / B2 = T 2/2} cosq_{1 / T} ^2/1 cosq₁

Verify Snell's law of refraction using Huygen's wave theory.

Let the surface AB represent a surface of separation of two media in which velocities of light are c1 and c2 respectively.

Let the wave front PQ be incident at an angle i to the surface AB. By the time Q reaches surface AB at S, the disturbance at P reaches R such that RS is the refracted wavefront.

The time taken by a ray to travel from T to U is

t = TO / C₁ + OU/C₂

= PO sin i /C₁ + OS.sin r / C₂

= PO SIN R /C₁ + (PS - PO) sin r / C₂

t = PO (sin i /C₁ - sin r /C₂) + PS. sin r / C₂

As the new wavefront is the forward envelop of all secondary wavelets, this implies that the time taken is independent of the position of O on the surface. Therefore, for t to be independent of O,

sin i / c₁ - sin r/c₂ = c

or sin i / sin r = c₁/c₂ = constant (m)

Find the position of an object which when placed in front of a concave mirror of focal length 20cm, produced a virtual image, which is twice the size of the object.

If the frequency of the incident radiation on the cathode of a photo cell is doubled, how will the following change :

(i) Kinetic energy of the electrons.

(ii) Photoelectric current,

(iii) Stopping potential.

(i) If the frequency of the incident radiation is doubled, the K.E. of the photoelectron becomes more than double. As the work function of a metal is fixed, so incident photon of higher energy will impart moe K.E. to the photoelectron.

(ii) Increase in the frequency does not change the photoelectric current. This is because incident photon of higher energy will not be able to eject more than one electron from the metal surface.

(iii) With the increase in frequency, K.E. of photoelectron increases, so stopping potential also increases.

Explain, with the help of a circuit diagram, why the output voltage is out of phase with the input voltage in a common emitter, transistor amplifier.

When a.c. signal is applied, the potential drop between collector and emitter is given by :

V₀ = V_CE = V_CC - I_CR_L

The positive half cycle of input a.c. voltage increases forward bias which increases the emitter current and hence the collector current. The increase in the collector current increases the potential drop across R_L which makes the output voltage less positive, thus giving negative a.c. output.

The negative half cycle of input a.c. voltage decreases the forward bias which decreases the emitter current and hence the collector current. The decrease in collector current decreases the potential drop across R_L which makes the output voltage more positive, thus giving positive a.c. output. Hence the output voltage is 180⁰ out of phase with the input voltage.

With the help of a labelled diagram, describe Millikan's oil-drop experiment for determining the charge of an electron.

The experimental arrangement used in Milikan's oil drop experiment is shown below :

Here A and B are two optically plane metallic discs of about 20 cm in diameter kept 1.5 cm apart. The upper plate A has a pin hole O in its centre. The plates are arranged inside a circular metal chamber, provided with two equally spaced windows around it, and is surrounded by an oil bath to keep its temperature constant. A high potential difference of the order of 10,000 volts is established between plates A and B.

Draw the curves showing the variations of inductive reactance and capacitive reactance, with applied frequency of an a.c. source. A capacitor, resistor of 5 W, and an inductor of 50 mH are in series with an a.c. source marked 100V, 50 Hz. It is found that voltage is in phase with the current. Calculate the capacitance of the capacitor and the impedance of the circuit.

OR

State Huygen's postulates of wave theory. Sketch the wavefront emerging from a (i) point source of light and (ii) linear source of like a slit.

Huygen's postulates of wave theory are as follows :

(i) Every point of the medium situated on the wave front acts a new wave-source from which waves, called secondary wavelets, originate.

(ii) The secondary waveletes travel in the medium in all directions with the speed of light.

(iii) The envelope of the secondary wavelets in the forward direction at any instant gives the new wavefront at that instant.

Explain the effect of introducing a dielectric slab between the plates of a parallel plate capacitor on its capacitance. Derive an expression for its capacitance with dielectric as the medium between the plates.

OR

Give the principle and explain the working of a van de Graaff generator with the help of a labelled diagram.

Van de Graff Generator - It is a device to produce high voltage so that charged particles may be energised.

It consists of a large bellow metal sphere A placed on insulting supports. An insulating belt moves over pulleys P1,P2. The positive charge is leaked on the belt from high voltage source. When the pulleys are driven with the help of motor the positive charge moves along with belt. As the charge enters the hollow sphere, +ve charge is induced on outer surface while negative on the inner surface. The inner surface charge is neutralised by +ve charge with the help of brushes B. As more and more charge is induced on the sphere its positive potential goes on increasing. To protect the leakage of charge to atmosphere the whole apparatus is enclosed in a cement and concrete compartment with high pressure nitrogen gas filled in. The positive charge or ions to be energised are placed in a long tube T.