SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS)
SECTION ‘B’ (SHORT – ANSWER QUESTIONS)
2.i) A galvanometer, having resistance son, deflects full scale for a potential difference.of 100mV across the terminals. What resistance should be connected to increase its range to 50 Volts?
ii) A rectangular bar of iron is 2 cmx2 cm is cross section and 20 cm long. What will be its resistance at 500°C? If'(l = 0.0052,,1
and p = 11×1 0-8m.
iii) An iron core solenoid with 500 turns has a cros section of 5cm2. A current of 2.3 ampere passing through it produces of flux of B = 0.53 Telsa. How large an e.m.f. is induced in it. if the current is turned off in 0.1 second? What is the self inductance of the solenoid?
xi) Prove mathematically that the radius of circular path for a charge moving In magneiIc fire ld IiS given by
If a particle of charge “q” enters a magnetic field of flux density ‘B with a velocity “V” along a path making an angle “e” with the direction of the field, its velocity may be resolved into two componenets Vx = V Coss paralled to the field and Vy = V Sine perpendicular to the field. The first component will not be affected by the field but provides translatory motion. The component Vy = V Sine perpendicular to B produces circular motion. Since centripetal force required for circular motion is provided by the magnetic force there fore
The superposition of translatory motion and circular motion results in a helix about B. The radius of helix is given by the above equation
xii) What happens to the temperature of a room in which an air conditioner is left running on a table in the middle of the room?
When on a.c is left running on a tabTe in the middle of a room, heat is removed from the room by the a.c. But, heat is rediated on the other side to the room by the condenser at the back. The heat pumped out the back of the a.c and into the room is greater than the heat pulled into the front of the unit, as work done to remove the heat from cold to hot puts into the room an additional ammount of heat is required.
OR Give the assumptions of special theory of relativity and discuss anyone of the results obtained.
Postulates of the special theory of relativity
In 1905 Einstein proposed his famous theory of special relativity. he
theory is named as special because of the reason that it is valid specially for inertial frames and it was modified into a general theory for accelerated frames of reference. This theory is based on two assumptions known as the postulates of special relativity, which are stated as:
There is no preferred or absolute inertial frame of reference i.e. all the inertial frames are equivalent for the description of all physical laws (Newton’s laws as well as Mqxwell’s electromagnetic equations).
The speed of light in vacuum is the same for all observers in uniform translational relative motion and is independent of the motion of the observer and the source.
The speed of light ‘c’ is a universal constant and its value is nearly equal to 3 x108 rns’.
Results of einstein’s theory of relativity:-
The special theory of relativity is developed with the concept that frames of reference are in relative motion with a constant speed ‘v’, If the speed v becomes large enough to approach the velocity of light c, then the Galilean. transformation are found to be reasonably wrong.
Thus a factor called as Lorenz Relativistic factor introduced.
It is in our common situation if v/c is much small then v2/c2 will
1. Mass Variation: If the rest mass of an object in a frame of reference at rest is ‘mo’ and this mass is measured by an observer moving with a constant velocity ‘v’ relative to the object, then it will not remain constant if the speed ‘v’ is comparable to ‘c’. The mass ‘rn’ in the moving frame will vary according to the mass variation relation given by
xiii) How can a galvanometer be converted into an ammeter? Derive the relevant expression.
Ammeter: Ammeter is a modified form of galvanometer used to measure electric current. It is connected in series to the circuit. Its
resistance must be low so that it can measures the current in the circuit accurately.
Conversion Of A Galvanometer Into A Ammeter: To convert a galvanometer into a ammeter a shunt R, of appropriate small resistance should be connected in parallel with the galvanometer.
Let a galvanometer G whose resistance is Rg and gives full scale deflection when current Ig flows through it. In order to convert it into. an ammeter which can measures current up to ‘1’, a shunt resistance Rs of small value is connected in parallel. The value of Rs is such that current Ig must passes through the galvanometer coil and the remaining current I-Ig passes through shunt Rs.
The potential difference across Rg and R, are given as:
From the above equation we can find a suitable value for the shunt (low resistance) to be used to convert a galvanometer into a ammeter.
xiv) Discuss the Principle of production of laser iight.
Laser: Defination: “The Laser is a device for producing very intense, highly directional, coherent and mono chromatic light beams”. Laser means light amplifycation by stimulated emission of radiation.
The Laser Principle: Consider an atom having electron in ground state. When electron absorbs energy equal to the difference E2 – El, it jumps into E2. Now atom in excited state, when on photon of energy exactly equal to the differences of two states (hv, E2 – El) is incident on it fig
(1). This incident photons increases the probability that the electron will retum to the ground state (El) by emitting a second photon having the same energy and. exactly in phase with the ancident photon fig (2). These two photons in their return stimulate other atoms to emit photons in a chain of similar events.
OR State Bohr’s postulates for Hydrogen atom. Ans: Bohr’s Atomic Theory:
An electron moves only in those circular orbits for which its angular momentum mvr is an integral multiple of h/27t. Where ‘h’ is planck’s constant.
xv) Define Motional e.m.f. and derive the relevant formula.
Definition: When a conductor is moved across a magnetic field with certain velocity, an e.m.f. is induced across its ends. This dynamically induced e.m.f. is known as “motional induced e.m.t:. The current that flows in a complete circuit is called “induced current”. Principle: Motional e.mJ. can be measured by determinating the work done as a certain amount of charge is carried from one end of the conductor to its other end when it is moved in a magnetic field.
Explanation: Let length of a conductor = L
Let strength of magnetic field = B
SECTION ‘C’ (DETAILED – ANSWER QUESTIONS)
3.a) On the basis of kinetic theory of gases, show that
PRESSURE OF THE IDEAL GAS:-
The force on unit area is known as the pressure of the gas
DERIVATION OF PRESSURE ON THE BASIS OF KINETIC’ MOLECULAR THEORY OF GASES:
According to kinetic molecular theory of gases, the molecules of a gas are in continuous random motion. They collide with each other and with the walls of the container- So they exert pressure on the walls of the container.
In order to derive an expression for the pressure of an ideal gas consider,
• N’ number of molecules contained in a cubical vessel whose walls are perfectly elastic
• The faces of the cube which are normal to the x-axis and having edge length L.
Now consider one molecule of the gas, having mass ‘m’ and moving
with a velocity ‘v’ which can be resolved into components v.. vy, Vz in the direction of the edqes. It collides with one face A of the cubical vessel. After collision it will bounce back such that its velocity ‘vx’ is reversed,
The Vy and v« component of the velocity will remain unaffected.
The momentum before collision = m v,
The momentum after collision = – m v,
Change in momentum = momentum after collision – momentum before collision.
Change in momentum = m v, – (- m v.)
Change in momentum = 2 m v.
The negative sign is introduced because of the reason of Lenz’s Law. According to which “an e.m.f. is induced ‘in lhe coil (conductor) if the number of lines of force linked with lhe coil is changing”.
The e.m.f. last so long as the change of the flux is in progress and becomes zero as soon as the flux through the coil becomes constant. The direction of the induced current is such that the magnet field it produces lends to keep the flux linkage constant
When two coils are placed close together than the changing current in one coil (primary) produces an e.m.f. in the near by coil (secondary).
This effect is known as “Mutual Induction”.
The mutual induction (M) between coils (conductor) is mathematically defined as
4.b) What is Compton Effect? Derive expression for the Compton shift in wavelength.
In 1924, Arthur Compton performed an experiment to confirm the particle like behavior of a photon. He observed mat when radiations like X-rays or y-rays fall on a stationary electron, they are scattered. The scattered photon has frequency less than the incident photon. This phenomenon i~ known as “Compton Effect”. Compton effect provided a
solid support for photon theory of light since the results obtained were
elegantly described by assigning to the photon an energy E = h u and
momentum P = h u/c
Compton effect cannot be explained on the basis of wave theory of
light. It can only be explained on the basis of quantum theory of·ligh~
The scattering is treated as a two body collision between a photon ano
electron. The collision is elastic, therefore the energy and momentum
both are conserved.
Compton assumed that an incident X-rtly photon collides with a
stationary light particle such as an electron then after the collision the
photon scatters at a certain angle with reduced energy and momentum.
During the collision a part of energy of photon is transferred to the
electron. The electron is treated at rest and because for high energy
photon, thJ initial motion of the electrons may be neglected.
It is sufficient to analyze the scattering process in a single frame of
reference. The photon approaches towards the electron with a
frequency U1 and is scattered at an angle 9 with a lower frequency U2.
After collision the electron recoils at a certain angle ct>.
The photon energies before and after collision are hU1 and hU2.
Where as the corresponding momentum’ are hu1/c and hU2/c. The
energy and momentum of the recoiled electron are E and P
respectively. Applying law of conversation of momentum we get:
Total momentum before collision = Total momentum after collision
The above equation is called as Compton formula for the increase in wavelength of the scattered photon. The quantity hllTloC in the above equation is called iJS Com ton wavelen th and is denoted by Ác
Compton Shift: Arthur Holy Compton in 1923 studied the scattering of X-rays by loosely bound electrons from a graphite target He found that wavelength ‘As’ of the scattered X-mys is larger than the wavelength ‘At’ of the incident X-rays. The increase in the wavelength of the scattered X-rays ’11).’ is known as “Compton’s Shift” for ,scattering angle ‘9’. Compton’s shift is given·by,
If the scattering X-ray photons are observed at 0 = 900 then Compton’s shift ‘M’ is equal to Compton’s wavelength.
OR What is a Camot Cycle. Derive expression for its efficiency.
A carnot engine consist of:
i) A cylinder which is provided with a light, frictionless nonconducting piston. The walls of cylinder are insulated and base is conducting to absorb or remove heat
ii) Art ideal gas is filled as a working substance at temperature T pressure P1 and volume V1.
iii) A hot bottom or source of large heat capacity.
iv) A cold body or sink of large heat capacity.
The operating cycle of camot engine is reversible and consists of following four processes of the working substance.
i) Isothermal expansion.
ii) Adiabatic expansion.
iii) Isothermar compression
iv) Adiabatic compression.
i) Isothermal expansion:
The gas is expand isothermally at temperature T1. absorbing heat O from the hot body. This process is isothermal and it is represented by curve AB
ii) Adiabatic expansion:
The gas is then expand adiabatically until its temperature reduce to T2. To maintain the intemal energy constant: the system is placed on an insulator during this process. It is represented by curve BC.
i) DUling all the four processes the thermal and mechanical equilibrium is maintained and the system comes back. to its initial state. There is no change in its intemal energy 6U=O
ii) The network done during one cycle equals to the area enclosed by the path ABCDA of the PV-diagram.
iii) Therefore no heat engiite· can be more efficient than camot engine operating between the same two temperatures because of friction and.other heat losses.
EFFICIENCY OF CARNOT ENGINE
i) The efficiency of heat engine depends on the temperature of hot and cold bodies.
ii) It is independent of the nature of working substance.
iii) The greater the difference between hot and cold bodies, the greater will be the efficiency of Camot engine.
iv) If the cold body is at 0 K then the efficiency of the Camot engine is 100% i.e, T2 = 0 K (Absolute Zero temperature) and the efficien~ of a Camot engine is less than 100 percent above absolute zero temperature of the sink. It means that efficiency can never be one or 100% unless cold body is at absolu.te zero tempera.ture (T2 = 0 K) Practically such resewoirs are not available and hence the . maximum efficiency is always less than one.
5.a} State Ohm’s law. Show that for a balanced Wheatstone bridge P R
Ohm’s law: Statement: The amount of current flowing through a conductor is directly proportional to the potential difference between its ends provided the physical condition does not change-
Wheatstone Bridge: -A wheat stone bridge is an instrument used to measure unkonwn resistance-
Wheatstone Bridge Principle: “If the rules of the resistance are such
then no current will flow through the galvonometer even Q X keys K1 and K2 are closed. Undr this condition the wheatstone bridge is said to be balanced. This is called wheatstone bridge principle.”
Constuction: If four resistance P, Q, R and X are connected end-toend to form a closed mesh or closed loop or bridge ABCDA. A cell is connected between A and C with a key K1, and a galvanometer is
connected between Band D with a Key K2. This circuit is known as , wheatstone bridge.
Proof: Under balanced condition when no current passes through galvanometer, the potential at point B & D must be same and the potential differences a cross galvanometer must be zero. Under this
condition the resistances P and Q are in series and the same current flows through these, suppose this current is 11. Also suppose thata current 12flows through R and X are also in series.
Potential difference between A and B, Potential difference between A and D.
5.b) Give the construction and working of Geiger counter, also draw the diagram.
Geiger Counter: Geiger countr is a portable device which is widely used for the detection of ionizing particles or radiations.
(i) It is a hollow metal cylinder one end of which is closed by an insulating cap. At the other end a thin sheet of mica is fixed through which the ionizing particles can enter.
(ii) An anode wire is placed along the axis of cylinder.
(iii) A mixture of argon and alcohol (or balogen) gas is filled at low pressure.
(iv) A large potential difference of about 1000 volts is applied across
the metal cylinder and anode wire.
(v) A resistance R of about 109 Q is connected in series with a battery and anode wire
Working: When an ionizing particles enter the tube through the window, it produces ions and eoectrons. These electrons are accelerated towards the anode wire and positive ions and towards the cathoti. The accelerated electrons suffer collisions with the gas molecules and produce furthur ionization. This gives rise to an electric discharge, and the gas becomes conducting. Consequently yurrents flows through R and voltage drop is developed across the resistance. This ends of Rare connected to a loudspeaker or an electronic counter. Thus each time a particle enters the counter an ionization current pulses occurs. Which gives click. in the loudspeaker or a count in the electronic counter.
OR W.hat is Nuclear fission? Explain Fission chain reaction.
Nuclear Fission: When a heavy nucleus is broken into two lighter nuclei, energy is released. This reaction is called “Fission Reaction”.
Explanation: When a uranium nucleus (92U235)is bombarded with a slow moving neutron, the uranium neucleus undergoes a nuclear fission and may produce two fragments 56Ba141 and 36Kr92along with three neutrons. Typical nuclear fission reaction are the following.
Chain Reaction: The formation of more than one energetic neutron induces fission in more nuclei and a chain reaction is develop. resulting in the sudden release of a huge amount of energy. Hence a self sustaining chain reaction will build up. The energy release in the fission process is due to the conservation of mass defect between the mass of the heavy nucleus and the resulting fragments, into energy.
The nuclear chain reaction may be schematically represented as shown In the figure.