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Physics Questions and Answers October 01, 2022

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A firework rocket is launched vertically. At the moment of explosion it is moving with a vertical speed of vo 2 ms upwards. The explosion releases an energy of Eexp 1 J and the rocket bursts into four pieces with masses of m 1g, m2 2g, m3 3g and m4 4g. The piece with mass m4 moves vertically upwards with a speed of v4 1 ms. The pieces of

(a) Find an expression for the angle for which the grey area A, is f times the area of the outer square Ag. Your expression for 8 should take the form 0B where B is a constant and C(f) is a function of f. State B and C(f) explicitly. You may assume that r 1, 1 and f 0. The value of TR indicates the radius of the outer circle. (b) Find the

The energy levels of the electron in a hydrogen atom are characterised by a quan tum number n En hcR where his Plancks constant, c is the speed of light and R is the Rydberg constant. (a) State a formula that relates the wavelength of light A to h, c and E which is the energy of a photon. (b) Let p and q be the quantum numbers of the upper and

A radioactive sample contains two isotopes, A and B. Isotope A decays to isotope B with a half life of t12. Isotope B is stable. (a) The number of atoms of A left after a time t is given by NA(t) NAO ext where NO is the initial number of atoms of A. Derive an expression for in terms of t12 (b) Initially the number of B atoms in the sample is

A long, thin, straight wire carrying an electric current I causes a magnetic field of flux density B at a perpendicular distance r from the wire. The magnitude of this flux density is given by the following relation A where a is a constant. The magnetic field points circumferentially around the wire. A second, identical wire is placed parallel to

An organ pipe is open at one end and closed at the other. The lowest note you can play on this pipe has frequency fmin. If the speed of sound in the pipe is v, what is the length L of the pipe A L V L B V Afmin L min L D 2v E L min 2

The acceleration g due to gravity on a spherical planet in any universe is given by GM R g where M is the mass, R the radius of the planet and G is the gravitational constant in that planets universe. In a different universe the gravitational constant is G and has twice the value of the gravitational constant in our Universe G. Find the ratio

3. Consider a system of many interacting particles. Let each particle have a potential energy V(r) with respect to any other particle, where V(r) x r where r is the distance to another particle and n is an integer. For such systems the Virial Theorem relates the time averaged total kinetic energy of all particles (Ttot) to the time averaged total

In a cathode ray tube, an electron (mass 9.1 x 1031 kg, charge 1.6 x 1019 C) is accelerated from rest by a uniform electric field of strength 20 kV m1. How much time does it take to travel 50 cm A B C 1.1 x 1018 s. 2.8 x 1016 g 1.7 x 108 s 5.3 x 107s D E 3.2 x 105 s 2

An asteroid of mass 10 kg is moving towards a space station at 1ms. It is proposed to stop it by firing a 1 MW laser at it. For how long must the laser be fired You may assume that the surface of the asteroid is perfectly reflective, all photons are incident perpendicular to the surface of the asteroid, and a photons momentum is related to its

An experimental setup consists of two deep tanks, each of width L, separated by a thin, transparent membrane, as shown in the figure below. The left tank is filled with a transparent liquid with refractive index 7, and the right tank with a transparent liquid with refractive index n. The membrane has refractive index 7. Assume that the refractive

22. The equation of circle C is 4x 24x 4y16y 43 0 while the equation of circle C is 4x 40x 4y8y 79 0. Sketch a diagram of these circles on the axes below, along with all lines which are tangent to both circles. For each line, calculate the length of the line segment joining the tangent points. y X 9

In a certain binary star system, two stars with identical mass m have equal and opposite velocities v2 on the opposite sides of the same circular orbit with radius R. In another system with three identical stars of the same mass m as before, it is observed that all three stars are equally spaced around a circular orbit with the same radius R as

Consider two sound waves travelling with the same speed and amplitude but having similar but slightly different wavelengths, A and 2, and angular frequencies, w and . The two waves are described with the functions y (x, t) Y2(x, t) What is the speed u in terms of the angular frequencies and wavelengths Sketch y y as a function of r, at some time

A parachutist jumps out of a plane at height h. She is subject to air resis tance with a force of av. The equation of her motion is given by What are the units of a du M dt mg av. Calculate the terminal velocity of the parachutist. Estimate how much work is done by the air resistance as she falls, assuming that she is falling at near terminal

A spring with spring constant k and natural length L joins two blocks of mass m and M. The two blocks lie on a horizontal table, initially L apart. The maximum force for static friction between a block and the table is given by the coefficient of static friction , multiplied by the blocks weight. How far must the mass M be displaced to cause mass

Person A is busy for 50 of the week, Person B 75, and Person C 20. If a time for a meeting is picked at random, what is the probability that (a) all three people are busy, and (b) all three people can attend the meeting 4

Consider the pulley system below supporting an object with mass m. As sume gravitational acceleration to be g, that the pulleys are massless and friction less, and the string is massless and inextensible. With how much force F must the string be pulled to keep the mass at the same height m force F A mg 3 B mg 2 C D E mg 2mg 3mg 2

21. A child of mass m stands on a platform which rotates freely at angular speed w. The childs centre of mass (COM) is initially at a radius of ro from the axis of the platform as shown in the figure below. The child now slowly pulls itself closer to the centre of the platform. COM m To (a) State the minimal force F(r) needed to pull the child

A and B are sets and they are defined below. Answer the following questions. (12 Points) U 1, 2, 3, 4, 5, f, b, 9, t, 0, j) A (1, 3, 5, f, b, t, 0 B 4, 5, 9, t, 1) a) BCA is it true or false b) AB c) BA d) AU

A centrifugal pump is discharging water at the rate of 100 liters/s. The internal and external diameters of the impeller are 150 mm and 300 mm respectively. The width of the impeller at inlet and outlet are 12 mm and 6 mm. The vanes are curved bade at 45 to the tangent at outlet. Find the increase in pressure as the water passes through the

An iron rod 4.00 m long and 0 . 500 cm 2 in cross-section stretches 1.00 mm when a mass of 225 kg is hung from its lower end. Compute Youngs modulus for the iron.

A load of 50 kg is applied to the lower end of a steel rod 80 cm long and0.60 cm in diameter. How much will the rod stretch? Y = 190 GPa for steel.

You add 1.00kg of ethylene glycol (C2H602) antifreeze to 4450g of water in your cars radiator. QUESTION 1. What are the boiling and freezing points of the solution

16.5 g of CO are dissolved in 500 mL of water, which has density 1.00 kg L1 at 20C. Assume that the total volume of the solution is 500 mL. (a) Calculate the molarity of the solution at 20 C (b) Calculate the molality of the solution at 20 C (c) What is the mole fraction of CO (d) What is the mole fraction of water

Biochemists have discovered more than 400 mutant varieties of hemoglobin, the blood protein that carries O. A physician dissolves 21.5 mg of one variety in water to make 1.50 mL of solution at 5.0 C. She measures an osmotic pressure of 3.61 torr. What is the molar mass of the protein II MRT

Hydrogen peroxide is a powerful oxidizing agent in concentrated solution in rocket fuels and in dilute solution as a hair bleach. An aqueous solution H202 is 30.0 by mass and has a density of 1.11gmL. Calculate its (a) molality (b) mole fraction of H202 (c) molarity (a) From mass to molality (molkg solvent),(b) From mass to mole fraction mol

Write down the Lagranges equation, when the Lagrangian function has the form, L min

Write down the Lagrangian and Lagranges. equation of a linear harmonic oscillatont.

The relation between water evaporated (W kg), coal consumption (C kg) and kWh generated per 8hour shift for a steam generating station is as follows W 13500 7.5 kWh....(i) C 5000 2.9 kWh....(ii) (i) To what limiting value does the water evaporating per kg of coal consumed approach as the station output increases (ii) How much coal per hour would

Find the order of magnitude of the number of table tennis balls that would fit into a typicalsize room (without being crushed).

Two identical 1 kg blocks of copper metal one initially at a temperature T oC and the other initially at a temperature T 100C are enclosed in a perfectly insulating container. The two blocks are initially separated. When the blocks are placed in contact, they come to equilibrium at a final temperature T The amount of heat exchanged between the

What is the range of wavelength of electromagnetic spectrum between which light lies O 3500 A t 7500 A O 3500 A t 7800 A 03800 Ao 1 7800 A O3500 A t 5000 A O 3200 A t 7500 A

Consider the discretetime system described by the statespace model xk 1 Axk Buk yk Cxk where 2 1 0 2 A H and x is the state vector, and u u1 Consider also the finite horizon cost functional given by J 2o (2x k 4x k u k) x 3 x 3. If the initial system state is given by x 0 2 3 9 9 B C 10, u is the input vector. and a control

Let PA represent the density of aluminum and Pre that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius Te on an equalarm balance.

A house is 50.0 ft long and 26 ft wide and has 8.0ft high ceilings. What is the volume of the interior of the house in cubic meters and in cubic centimeters

A solid piece of lead has a mass of 23.94 g and a volume of 2.10 cm. From these data, calculate the density of lead in SI units (kilograms per cubic meter).

The lift pump is effective for pumping water as long as the well is less than 10m deep. Explain.

State the density property of a barometer liquid and explain its effects. Explain in detailed.

A monochromatic beam of light travels through air of refractive index na and strikes a liquid of refractive index ny at an angle of incidence as shown in the figure below. At the bottom of the tank which contains the liquid is a plane mirror at angle o to the horizontal. The tank can be considered infinitely long. Beyond a certain value of the

Mars moons Phobos and Deimos are in equatorial, nearcircular orbits around Mars. They both orbit in the direction of the planets rotation. Phobos has an orbital period of 13 of a Martian day, and Deimos has an orbital period of 54 Martian days. An astronomer on Mars, near the equator, observes both moons during the course of a Martian night. (a)

The Euler number E, has no units. It is used in fluid flow calculations. It depends on the pressure P, density p, and fluid velocity v such that where a, b and c are constants. Eu Pape Find the ratio of a b c in its simplest form, where a, b and c are positive or negative integers.

17. As indicated in the figure, a motor bike of total mass m (m is the mass of bike plus rider) is ridden along a horizontal trajectory of radius R on the inside of a cylindrical cage. trajectory R bike a The bike and the rider are inclined at an angle a to the wall. The angles a that the bike can make with respect to the walls of the cage are

Consider a set of masses of three different values ma, me and me. Each of the following three combinations have the same total mass. 1. two masses of ma plus three masses of mi 2. five masses of ma plus one mass of me 3. two masses of ma plus one mass of m, plus one mass of me Find mb and me in terms of ma 4

The above figure depicts a ball of mass m which is equipped on its lower side with a massless spring of uncompressed length Lo and spring constant k. The spring is initially compressed to a length L Lo, as shown in the figure. The ballspring system is either dropped vertically or launched with a horizontal speed to from a height of ho at a

Ten students need to complete their compulsory practicals for their high school examinations as detailed in the table below No. of students No. of different practicals to complete 1 2 4 4 3 B The school only has one laboratory in which several different experiments can be set up simultaneously. A maximum of six students are allowed in the schools

A particle of type X decays with equal probability either to a pair of particles of type Y or a pair of particles of type Z. Both Y and Z particles are stable. The decays of two X particles are observed. A pair of Y particles is found among the decay products. What is the probability that a pair of Z particles is among these decay products 14 13

The potential energy for a system of two atoms separated by a distance x is U(x) (shown below). Sketch What does this new curve represent physically and what does the point to repre sent du U(x) Xo X 2 2

(a) Sketch the functions f(x) x 2x 7 and g(x) 2 on the same graph. (b) Determine the coordinates of the points of intersection of the two curves and label their exact values. You are not required to determine coordinates of intersections with zor y axes. (c) Evaluate the finite area enclosed between the two curves. You are expected to show

Expand (a bx), where c is a positive integer, as a polynomial in z up to and including terms involving . If the coefficient of the r term is equal to band the coefficient of the term is, find a and c. 4

Sand is poured at a constant rate onto a flat horizontal surface. It forms a pile in the shape of a cone with a constant slope. (a) If r is the radius of the base of the cone, find how r varies with t, given that r(0) 0. (b) If it takes a time t for r to reach ri, how long does it take for the radius to reach 2r1 (in terms of t) 3 2

17. In Einsteins theory of gravity, light passing a star of mass M, at a distance R from the centre of the star, is bent by an angle (measured in radians, 27 radians 360) as shown in the diagram. (a) Assume that depends on the gravitational constant G and also depends on the mass of the star M, the distance R and the speed of light c 3 108 ms ,

A vehicle travels in a fixed direction at a velocity v(t) that varies with time as follows t t t v(t) At v(t)CB(tt) v(t) v. Here A, B, C and v2 are constants. (a) Find A. B and C such that both the velocity and acceleration are continuous at t t and t t. (b) Sketch the velocity and acceleration as a function of time. (c) Find the total

15. The observed brightness of a Sunlike star shows periodic dips. The time period between these dips T 225 days. (a) If these dips are interpreted as being due to the transits of a planet in a circular orbit around the star, estimate the radius R of that orbit. You may assume that the star has the same mass as the Sun and that the planets mass

14. A machine requires 10kW of electrical power when operating at 100V. (a) If power is delivered through a cable with resistance 10002, how much power is lost to the cables resistance (b) In order to reduce power loss, a transformer is used between the cable and the machine. What ratio of turns is required on the transformer in order to reduce

(c) Assume that the effects in part (a) and (b) can be combined to give a total diameter 83, where s 8 8. Find the pinhole size that produces the sharpest image of the light source on the screen. 4,21. A pinhole camera consists of a box with a small aperture (of diameter z). A point light source P is at a distance u from the aperture outside the

A toilet roll is made up of an inner cardboard tube, diameter z cm, with toilet paper wrapped around it to give an overall diameter of y cm. The length of the card board tube is z cm. Suppose the diameter of the inner tube is reduced from a cm to (x1) cm, but the volume of toilet paper is kept the same. What is the difference in the total volume

Which of the following integrals are equal to zero (you do not need to evaluate the integrals explicitly) 1. 2 sin (3x) da 2. 3. f cos x da 4. 11 x da 5. 90 90 2 dz sin (52) sin a dr A B D E 1,2 3,4 1 1,2,5 1,5 2

The number of atoms N in a sample of a radioactive substance z decays with time according to the equation, N(t) N(0)et where N (0) is the number of atoms at time t 0 and X, is a constant for substance x. The halflife of a substance is defined as the time taken for N to reach half of its initial value. Substance a has a halflife of 1 hour. 36 of

Find the Calibrated LiftOff Speed KCAS using the chart below, which is a typical example of an aircraft position error correction chart. (Consider that the gear would obviously still be in the down position at lift off). Keep in mind the instructions said the given liftoff speed is 150 KTS. Landing Configuration curve is the same as a Takeoff
Find the Calibrated Lift-Off Speed [KCAS] using the chart below, which is a typical example of an aircraft

A ball of mass 2m slides along a frictionless track with speed u. Starting from a long distance away, it collides elastically with a stationary ball of mass m. (a) Calculate the final speeds of both balls (you may neglect any rotation of the balls). (b) If both balls were now positively electrically charged, describe qualitatively either how the

Following Bohr, we assume that a hydrogenlike atom may be modelled as a single electron (mass m and charge e) in a circular orbit around a much more massive nucleus (charge Ze). (a) By balancing forces, find the speed v of the electron in terms of its orbital radius. (b) Show that the total energy of the electron is equal to the negative of its

Consider the function Q f(x) x2 in the region 0, where P, Q and R are all positive constants. (a) Find an inequality satisfied by P, Q and R in order for f(x) to have at least one real root. R (b) Find a relationship between P, Q and R in order for f(x) to have exactly one stationary point. (c) If the relationshiop of the previous part holds,

17. Four circles of radius r1 are inscribed inside a square of side 4r1 as shown in the diagram below. (a) What is the radius r2 of the largest circle that can fit in the space at the centre of the square, bounded by the outer circles (b) If 8 spheres of radius r are now similarly arranged inside a cube of edge length 4r, what is the radius r3 of

A projectile is launched at speed u and angle 0 (as measured from the horizontal) outwards from the top of a high cliff. (a) Sketch the trajectory of the projectile for launch angles 05, 45 and 85. Use r(t) for the horizontal displacement from the launch point and y(t) for the vertical displacement from the launch point. (b) Using separate axes,

The Trojan asteroids share Jupiters orbit around the Sun approximately circular with a mean radius 5.2 AU (1 AU 1.5 x 10 m is the mean radius of the Earths orbit around the Sun). The Trojans are clustered around two points labelled L4 and L5, where the L4 point is 60 ahead of Jupiter in its orbit and the L5 point is 60 behind Jupiter in its orbit.

Two moons occupy circular orbits around a planet. The smaller moon has mass 1.5 x 105 kg and orbital radius 2.3 x 104 km. The larger moon has mass 1.1 x 106 kg and orbital radius 9.4 x 10 km. If the gravitational force exerted by the planet on the smaller moon is 1014 N, what force does the planet exert on the larger moon A B C D E 1.8 x 105 N 4.4

State the reason for the rise in the levels of the liquids when air is sucked from the tubes. Explain in detailed.

State two factors that should be controlled in manufacturing a cylindrical container of uniform thickness, which should normally be in a standing position. Explain in detailed.

An object Kept in large room having, T 25 oC takes 12 min to cool from 80 oC to 70 oC, The time taken to cool for the Same object from 70voC to 60 oC would be nearly

The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The

An extended object is placed at point O, 10 cm in front of a convex lens L and a concave lens L is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is L L Of (A) 0.4 O 10 cm (B)

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is Vo. A hole with a small area a4R(a 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct A. The magnitude of electric field at a point, located on a line

A heavy nucleus Q of halflife 20 minutes undergoes alphadecay with probability of 60 and betadecay with probability of 40. Initially, the number of Q nuclei is 1000. The number of alphadecay of Q in the first one hour is (A) 50 (B) 75 (C) 350 (D) 525

A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as T (t) To (1 Bt4) where is a constant with appropriate dimension while To is a constant with dimension of temperature.

In a radioactive sample K nuclei either decay into stable Ca nuclei with decay constant 4.5 x 1010 per year or into stable Ar nuclei with decay constant 0.51010 per year. Given that in this sample all the stable Ca and Ar nuclei are produced by the K nuclei only. In time t x 10 years, if the ratio of the sum of stable Ca and Ar nuclei to the

The magnitude of q is,In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q C. Then S is switched to position Q. After a long time, the charge on the capacitor is q C. IV P 192 www. lF 252 www 2V

A conducting wire of parabolic shape, initially y x, is moving with velocity V Vi in a magnetic uniform field B. (1 (2)) k non BB 1 Bo, L and are positive constants and A is the potential difference developed between the ends of the wire, then the correct statement(s) isare A. A is proportional to the length of the wire projected on the yaxis.

The magnitude of q2,In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q C. Then S is switched to position Q. After a long time, the charge on the capacitor is q C. IV P 192 www. lF 252 www 2V

A thin convex lens is made of two materials with refractive indices n and n2, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. fis the focal length of the lens when n n n. The focal length is f Af when n n and n n An. Assuming An

The value of Ris meter.,Two point charges Q and Q(3012 are placed in the xyplane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V 0 in the xyplane with its center at (b, 0). All lengths are measured in meters. y Q3 X

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T and T of different materials having water contact angles of 0 and 60, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is (are) correct Surface tension

A charged shell of radius R carries a total charge Q. Given as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) isare correct A. The dimension of energy is L B. The dimension of force is L C. The dimension of power is L5 D. The dimension of linear momentum is L

In the circuit shown, initially there is no charge on capacitors and keys S and S are open. The values of the capacitors are C 10 F, C 30 F and C3 C4 80 uF. Which of the statement(s) isare correct C 70 2 C 5V S 30 S2 10V 30 ww C3 www 100 2 Q A. The key S is kept closed for long time such that capacitors are fully charged. Now key S is closed,

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V T) diagram. The correct statement(s) isare R is the gas constant 2Vo Vo T2 A. Work done in this thermodynamic cycle (123 4 1) is W 1 Q2 Q23 B. The ratio of heat transfer during processes 1 2 and 2 3 is Q2 1 C. The above

Two identical moving coil galvanometers have 10 22 resistance and full scale deflection at 2 A current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohms law experiment with R

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area 0.5 cm and, 60 length 3 m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30 and 60, respectively. If elongation in copper wire is (Alc) and elongation in

A particle is moved along a path ABBCCDDEEFFA, as shown in figure, in presence of a force F(ay 2axj)N, where x and y are in meter and a 1 Nm. The work done on the particle by this force F will be Joule. 1.0 0.5 y A 0 F D E 0.5 B 1.0 X

A train S1, moving with a uniform velocity of 108 kmh, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 kmh towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats

A liquid at 30C is poured very slowly into a Calorimeter that is at temperature of 110C. The boiling temperature of the liquid is 80C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50C. The ratio of the Latent heat of the liquid to its

A planar structure of length L and width W is made of two different optical media of refractive indices n 1.5 and n 1.44 as shown in figure. If L W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For L 9.6 m, if the incident angle 0 is varied, the maximum time

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region d between the plates is filled with N dielectric layers, parallel to its plates, each with thickness 8 The N For a very large N(10), the capacitance C is m dielectric constant of the mth layer is K K 1 m N d In 2 Eo is the permittivity of free

a) Define the resolving power of microscope. Deduce an expression for it. b) A microscope is used to resolve to self luminous objects separated by distance of 4.0 x 105 cm. If the wavelength of light is 5461. Find the angle subtended at the eye by these objects when viewed at distance of distinct vision 25 cm. (10M) (4M)

a) Explain the formation of Newtons rings with reflected monochromatic light. (10M) Discuss why Newtons rings are in circular. b) In Newtons rings experiment the diameter of the 15th ring was found to be 0.590 (4M) cm and that of the 5th ring 0.336 cm. If the radius of the plano convex lens is 100 cm, calculate the wavelength of the light used.

a) Discuss the Fraunhofer diffraction at a single slit. Obtain the condition for principal maximum and minimum. (10M) b) A plan wave of wavelength 5893 x 108 cm is incident normally on slit of width (4M) 0.5 mm and forms a diffraction pattern on a screen placed 1 m away from the slit. Calculate the separation of first dark band on either side of

a) Explain the determination of Hall co-efficient, carrier concentration and mobility of charge carriers of a semi conductor. (10M) b) An electric field of 100 V/m is applied to a sample of n-type semiconductor whose Hall coefficient is -0.0125 m3 /C. Determine the current density in the sample assuming e 0.6 m2 / V.s.

a) Qualitatively analyze the diffraction pattern obtained when a plane diffraction (10M) grating is exposed to monochromatic light of wavelength, . b) A transmission grating has 8000 rulings per cm. The first order principal (4M) maximum due to a monochromatic source of light occurs at an angle of 30. Determine the wavelength of light.

a) Describe Newtons rings method for measuring the wavelength of monochromatic (10M) light. Give the necessary theory. b) In Newtons rings experiment the diameter of the 15th ring was found to be 0.590 (4M) cm and that of the 5th ring 0.336 cm. If the radius of the plano convex lens is 100 cm, calculate the wavelength of the light used.

a) Derive Maxwells equations from the basic laws of electromagnetism. Explain (10M) physical meaning of each equation. b) What do you understand by the gradient of a scalar field Explain its physical (4M) significance.