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Physics Questions and Answers September 27, 2022

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A contour integral is defined as I.n fai.c (dz(zn) pai ) where n is a positive integer and C is the closed contour, as shown in the figure, consisting of the line from 100 to 100 and the semicircle traversed in the counter clockwise sense. YA 100 The value of (in integer) is l z xiy 100

The circuit shown is in a uniform magnetic field that is into the page and is decreasing in magnitude at rate of 150 teslasecond. The ammeter reads 5.0 V

In a doubleslit interference experiment, d is the distance between the centers of the slits and w is the width of each slit, as shown in the figure above. For incident plane waves, an interference maximum on a distant screen will be missing when A. d 2 w B. d 3 w C. 2d w D. 2d 3w E. 3d 2w

Which of the following is most nearly the mass of the Earth (The radius of the Earth is about 6.4 106 m) A. 6 x 1024 kg B. 6 x 107 kg C. 6 x 103 kg D. 6 x 1033 kg E. 6 x 1036 kg

An engine absorbs heat at a temperature of 727C and exhaust heat at a temperature of 527C. If the engine operates at maximum possible efficiency, for 2000 joules of heat input the mount of work the engine performs is most nearly A. 400 J B. 1450 J C. 1600 J D. 2000 J E. 2760 J

The total energy of a blackbody radiation source is collected for one minute and used to heat water. The temperature of the water increases from 20.0C to 20.5C. If the absolute temperature of the blackbody is doubled and the experiment repeated, which of the following statements would be most nearly correct A. The temperature of the water would

Two large conducting plates form a wedge of angle a as shown in the diagram above. The plates are insulated from each other one has a potential V, and the other is grounded. Assuming that the plates are large enough so that the potential difference between them is independent of the cylindrical coordinates z and p, the potential anywhere between

Photobucket A. RC B. RC2 C. RC4 D. RC In 2 E. 12 RC In 2 R The capacitor in the circuit shown above is initially charged. After closing the switch, how much time elapses until onehalf of the capacitors initial stored energy is dissipated

Two positive charged of q and 29 coulombs are located on the xaxis at x 0.5a and 1.5a respectively, as shown above. There is an infinite grounded conducting plane at x o. What is the magnitude of the net force on the charge q A. B. C. D. E. 1 q 470 a 1 3q 202 1 2q 470 a 1 3q 470 a 29 0.5a a 1.5a 1 7q 202

A coaxial cable having radii a, b, and c carries equal and opposite currents of magnitude i on the inner and outer conductors. What is the magnitude of the magnetic induction at point P outside of the cable at a distance r from the axis A. Zero B. CHi 2r D. Hoir E. Hoi e 2r c62 bucket ba 2r c6

Consider the eight n 2 states. Find the energy of each state under weak Zeeman splitting and construct a diagram to show how the energies evolve as Bo increases. Label each line clearly and indicate it slope.

(4) For the Centaur rocket use the data given below: Initial mass m0 = 2.72 106 kg Mass at burn-out velocity, mg = 2.52 106 kg Relative velocity of exhaust gases v, = 55 km/s Rate of change of mass, dm/dt = 1290 kg/s Find (a) the rocket thrust, (b) net acceleration at the beginning, (c) time to reach the burn-out velocity, (d) the burn-out

A rocket has an initial mass of m and a burn rate of a = -dm/dt (a) what is the minimum exhaust velocity that will allow the rocket to lift off immediately after firing? Obtain an expression for (b) the burn-out velocity; (c) the time the rocket takes to attain the burn-out velocity ignoring g; and (d) the mass of the rocket as a function of

Consider the eight n 2 states. Find the energy of each state under strongfield Zeeman splitting. Express each answer as the sum of three terms The Bohr energy, the fine structure contribution and the Zeeman contribution. If you ignore fine structure altogether, how many distinct levels are there and what are their degeneracies

Explain the Zeeman effect and and its limitations with respect to magnetic field.

Obtain the Hamilton's equations for a particle of mass moving in a plane about a fixed point by an inverse square force-k/2. Hence (i) obtain the radial equation of motion, (ii) show that the angular momentum is constant (10 marks)

Consider a particle of mass m moving in a plane under the inverse square force 2 directed to the origin. Obtain the Lagrangian and Lagrange's equation of motion of the particle. (10 marks)

A car travels with constant speed on a circular road on level ground. In the diagram above, Fair is the force of air resistance on the car. Which of the other force shown best represents the horizontal force of the road on the cars tires

(b) Show that the centre of mass of a system of particles moves as if the total external force were acting in the entire mass of the system concentrated at the center of mass(7 marks) (c) The position vectors of masses 2 kg, 3kg and 4kg are 2i-3j, i+j+k and 4j+3k respectively. If their respective velocities are -31, 6j and 2i+3k units, calculate

(f) State any two Kepler's laws regarding planetary motion. (2 marks) (g) A passenger in a train moving at 30m/s passes a man standing on a stationary platform at t=t'=0. Twenty seconds after the train passes him, the man on the platform determines that a bird flying along the tracks in the same direction as the train is 800m away. What is the

The thermal and electrical conductivities of copper at 20C are 380 Wm-1 K-1 and 5.67 107 -1 m-1 number. respectively. Calculate the Lorentz number

Copper has electrical conductivity at 300 K as 6.40 107 m-. Calculate the thermal conductivity of copper.(Lorentz number is 2.44 10-8 W k).

Calculate the Fermi energy of copper at 0 K if the concentration of electron is 8.5 1028 m-3.

The mobility of electrons in copper 3103m2V-1s-1 assuming e=1.610-19C and me=9.110-31 kg. Calculate the mean collision time.

The thermal conductivity of a metal is 123.92 Wm-K-. Find the electrical conductivity and Lorentz number when the metal posses relaxation time 10-14 sec at 300 K. (Density of electron = 61028 per m)

Find the velocity of copper wire whose cross-sectional area is 1 mm when the wire carries a current of 10 A. Assume that each copper atom contributes one election to the electron gas.

Which two of the following circuits are highpass filters A. I and II B. I and III C. I and IV D. II and III E. II and IV 1. III. In In m Out Out II. IV. In In www Out Out

An AC circuit consists of the elements shown above, with R 10,000 ohms, L 25 millihenrie and C an adjustable capacitance. The AC voltage generator supplies a signal with amplitude of 40 volts and angular frequency of 1,000 radians per second. For what value of C is the amplitude of the current maximized

An alternating current electrical generator has a fixed internal impedance RgjXg and is used to supply power to a passive load that has an impedance Rg jx,, where j (1). Rg 0 and Xg 0. For a maximum power transfer between the generator and the load, X, should be equal to A. 0 B. Xg C. Xg D. Rg E. Ra

In the RLC circuit shown, the applied voltage is e(t) Em cos wt For a constant m, at what angular frequency w does the current have its maximum steadystate amplitude after the transients have died out D. V(1LC) (R2L)2 E. V(1RC)2 (LR) L

The magnitude of the force F on an object can be determined by measuring both the mass m of an object and the magnitude of its acceleration a, where F ma. Assume that these measurements are uncorrelated and normally distributed. if the standard deviations of the measurements of the mass and acceleration are om and a respectively, then oFFis A. B.

6. A conducting rod contains 8.5 1028 electrons/m. Calculate its resistivity at room temperature and also the mobility of electrons if the collision time for electron scattering is 2 10-14 sec.

A rigid cylinder rolls at constant speed without slipping on top of a horizontal plane surface. The acceleration of a point on the circumference of the cylinder at the moment when the point touches the plane is A. directed forward B. directed backward C. directed up D. directed down E. zero

The Fermi temperature of a metal is 24600 K. Calculate the Fermi velocity.

Consider a particle moving without friction on a rippled surface, as shown above. Gravity acts down in the negative h direction. The elevation h(x) of the surface is given by h(x) d cos (kx). If the particle starts at x 0 with a speed u in the x direction, for what values of u will the particle stay on the surface at all times A. v gd B.v gk

Free electron density of aluminum is 18.1 1028 m-3. Calculate its Calculate its Fermi energy at 0 K. [Planck's constant and mass of free electron are 6.62 10-34Js, and 9.1 10-34Kg]

A particle of unit mass undergoes onedimensional motion such that its velocity varies according to v(x) x where and n are constants and x is the position of the particle. What is the acceleration of the particle as a function of x A. nx2n1 B. nxn1 C. nexn D. 3xn1 E. 8x2n1

Calculate the drift velocity of the free electrons (with a mobility of 3.5 10-3 m V-1 s-1) in copper for an electric field strength of 0.5 V m-.

A block slides along a frictionless surface with a constant acceleration of 2 ms. At time t Os the block is at x 5m and travelling with a velocity of 3 ms. a) Where is the block at t 2 seconds b) What is the blocks velocity at 2 seconds c) Where is the block when its velocity is 10 ms d) How long did it take to get to this point X0 t0s 5 V3ms

Use the Fermi distribution function to obtain the value of F(E) for E - EF - EF = 0.01 eV at 200K.

For a Shelby tube, given outside diameter 3 in. and inside diameter 2.874 in. What is the area ratio of the tube

Which of the following best illustrates the acceleration of a pendulum bob at points a through e (A) (D) (C) C (B) AN

Two lenses are connected which have focal lengths 5 cm and 10 cm respectively. What will be the effective focal length?

Suppose that f(theta) 3 cos theta sintheta (i) Show that f(theta) a b. cos 2theta, where a and b are integers which should be found. (ii) Using your answer to part (a) and integration by parts, find the exact value of 6. 0 f(0) de

Consider the quasistatic adiabatic expansion of an ideal gas from an initial state i to a final state f. Which is the following statements is NOT true A. No heat flows into or out of the gas. B. The entropy of state i equals the entropy of state f. C. The change of internal energy of the gas is PdV. D. The mechanical work done by the gas is PdV.

The adiabatic expansion of an ideal gas is described by the equation PVY C, where y and C are constants. The work done by the gas is expanding adiabatically from the state (Vi, P) to (Vf, Pf) is equal to A. PfVf B. 12(Pi Pf)(Vf Vi) C. (PfVf PV)(1y) 1 D. P(V YV Y)(1y) E. Pf(VfYV)(1y)

Use the substitution x 2 sin theta to find the exact value of integration 0 to 1 1(4x)32 dx

To get to the top of a hill, a skier of mass 68.0 kg holds on to a rope and is puted up the slope by a motordriven winch at the top of the hill that winds the rope onto a drum. 30.0 (a) How much work is required to pull the skier 90.0 m along a 30.0 frictionless slope at a constant speed of 2.20 ms Express your answer in kJ. (b) What power must

The dispersion law for a certain type of wave motion is w (ckm) 2, where w is the angular frequency, k is the magnitude of the propagation vector, c and m are constants. The group velocity of these waves approaches A. Infinity as k o and zero as k B. Infinity as ko and c as k C. c as k o and zero as k D. Zero as ko and infinity as k E. Zero
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A second order differential equation is given by dydx2 dydx 56yx2x3 (a) Find the general solution of the differential equation.,dy (b) Find the particular solution for which y 0 and dr 0 when x 0.

A thin plate of mass M, length L, and width 2d is mounted vertically on a frictionless axle along the zaxis. Initially the object is at rest. It is then tapped with a hammer to provide a torque t, which produces an angular impulse H about the zaxis of magnitude H f t dt. What is the angular speed w of the plate about the zaxis after the tap A.

The dispersion curve shown above relates the angular frequency to the wave number k. For waves with wave numbers lying in the range ki k k2 which of the following is true of the phase velocity and the group velocity A. They are in opposite directions. B. They are in the same direction and the phase velocity is larger. C. They are in the same

Two point charges with the same charge Q are fixed along the xaxis and are a distance 2R apart as shown. A small particle with mass m and charge q is placed at the midpoint between them. What is the angular frequency w of small oscillations of this particle along the ydirection B. C. E. 29 2Tom R2 29 4 com R Qq 2Tom R Qq 4Team R tobucket Qq 27om R

A. V(t) B.V (t) If n is an integer ranging from 1 to infinity, is an angular frequency, and t is time, then the Fourier series for a square wave, as shown above, is given by which of the following C. V(t) D.V (t) 4 7 sin(not) n 1 (2n 1) cos(nwt) n 4 E. V(t) 1 (2n1) Ik V(t) sin((2n 1) wt) otobucket 4 cos(nwt) cos((2n 1) wt) ela
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Two pendulums are attached to a massless spring, as shown above. The arms of the pendulums are of identical lengths 1, but the pendulum balls have unequal masses m and m. The initial distance between the masses is the equilibrium length of the spring, which has spring contant K. What is the highest normal mode frequency of this system A. g1 K mi

(b) Show the four roots of f(x) 0 on a single Argand diagram.,The polynomial f is given by f(x)x43x 15x 99x 130 (a) Given that x 32i is a root of the equation f(x) 0, use algebra to find the three other roots of the equation f(x) 0.

A bead is constrained to slide on a frictionless rod that is fixed at an angle with a vertical axis and is rotating with angular frequency w about the axis, as shown above. Taking the distances along the rod as the variable, the Lagrangian for the bead is equal to A. 12 ms 2 mgs cos 0 B. 12 ms 2 12 m(ws) mgs C. 12 ms 2 12 m(ws cos 0)2 mgs cos

A string consists of two parts attached at x o. The right part of the string (x 0) has mass , per unit length and the left part of the string (x

cm Oscillation A. 5V, 250Hz B. 1.5V, 250Hz C. 5V, 6Hz D. 2.5V, 83Hz E. 6.14V, 98Hz 5 thu phobucket os store, share. 2 3 4 5 6 The figure above represents the trace on the screen of cathode ray oscilloscope. The screen is graduated in centimeters. The spot on the screen moves horizontally with a constant speed of 0.5 centimetermillisecond and the
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A rectangular loop of wire with dimensions shown above is coplanar with a long wire carrying current I. The distance between the wire and the left side of the loop is r. The loop is pulled to the right as indicated. What is the magnitude of the net force on the loop when the induced current is i A. B. Poil D. 2T Poil 2 In n () (a) In C. Hoil b 2

When alpha particles are directed onto atoms in a thin metal foil, some make very close collisions with the nuclei of the atoms and are scattered at large angles. If an alpha particles with an initial kinetic energy of 5 MeV happens to be scattered through an angle of 180, which of the following must have been its distance of the closest approach

The components of the orbital angular momentum operator L (La Ly, L.) satisfy the following commutation relations. Lz, Ly ihLz Ly, L iL Lz, Lx ihLy What is the value of the commutator L, Ly, L A. 2ihL, Ly B. i(L2 L) C.ih (L L2) D. i(LL2) E.ih (LL2) (GI

A hoop of mass M and radius R is at rest at the top of an inclined plane. The hoop rolls down the plane without slipping. When the hoop reached the bottom, its angular momentum around its center of mass is A. MRV (gh) B. 12 MRV (gh) C. M(2gh) D. Mgh E. 12 Mgh

A transition in which one photon is radiated by the electron in a hydrogen atom when the electrons wave function changes from to , is forbidden if y, and y A. have opposite parity B. are orthogonal to each other C. are zero at the center of the atomic nucleus D. are both spherically symmetrical E. are associated with different angular momenta

An industry survey of people in sales management positions gave the number of years of experience in sales related positions as shown below. Males Females Sample size 90 80 Mean years 25.7 22.5 Standard deviation years 8.2 3.5 (a) Construct a 95 confidence interval for the difference of population means.,(b) Perform a test to determine if the mean

The spacing of the rotational energy levels for the hydrogen molecule H2 is most nearly A. 10 eV B. 103 eV C. 10 eV D. 10 MeV E. 100 MeV

The configuration of three electrons is 1s2p3p has which of the following as the value of its maximum possible total angular momentum quantum number A. 72 B. 3 C. 52 D.2 E. 32

In a 3S state of the helium atom, the possible values of the total electronic angular momentum quantum number are A. o only B. 1 only C. 0 and 1 only D. 0, 12, and 1 E. 0, 1, and 2

Two small pith balls, each carrying a charge q, are attached to the ends of a light rod of length d, which is suspended from the ceiling by a thin torsion free fiber, as shown in the figure. There is a uniform magnetic field B, pointing straight down, in the cylindrical region of radius R around the fiber. The system is initially at rest. If the

Two ions 1 and 2, at fixed separation, with spin angular momentum operators S, and S, have the interaction Hamiltonian H JS S, where Jo. The values of S2 and S2 are fixed at S(S 1) and S(S 1), respectively. Which of the following is the energy of the ground state of the system A. O B.JSS C. JS(S1)S(S 1) D. (J2) (SS) (S S 1) S(S1) S(S1) E.

Positronium is the bound state of an electron and a positron. Consider only the states of zero orbital angular momentum l o. The most probable decay product of any such state of positronium with spin zero (singlet is) A. o photons B. 1 photons C. 2 photons D. 3 photons E. 4 photons

At a given instant of time, a rigid rotator is in the state y(0, 0) (47) sin sin o, where is the polar angle relative to the zaxis and is the azimuthal angle. Measurement will find which of the following possible values of the zcomponent of the angular momentum L A. O B. 2, 2 C. , D. 2, 2 E. , o,

A diatomic molecules is initially in the state (0, 0) (5 37 2Y5)(38)2 where Y is a spherical harmonics. If measurements are made of the total angular momentum quantum number I and of azimuthal angular momentum quantum number m, what is the probability of obtaining the results 1 5 A. 361444 B. 938 C. 1338 D.5(38)2 E. 3438

A uniform silver wire has a resistivity of 1.54x108 m at room temperature. For an electric field along the wire of 1 volt cm, compute the average drift velocity of electron assuming that there is 5.8 1028 conduction electrons m. Also calculate the mobility.

Two uniform cylindrical disks of identical mass M, radius R, and moment inertia 12MR collide on a frictionless, horizontal surface. Disk I, having an initial counterclockwise angular velocity wo and a centerofmass velocity Vo 120 R to the right, makes a grazing collision with disk II initially at rest. If after the collision the two disks stick

Which of the following is NOT compatible with the selection rule that controls electric dipole emission of photons by excited states of atoms A. An may have any negative integral value B. Al 1 C. Am 0, 1 D. As 1 E. Aj 1

An energylevel diagram of the n 1 and n 2 levels of atomic hydrogen (including the effect of spinorbit coupling and relativity) is shown in the figure. Three transitions are labeled A, B, and C. Which of the transitions will be possible electricdipole transition

Which is the following is the orbital angular momentum eigenfuction Y (0,6) in a state for which the operators L and L, have eigenvalues 6 and respectively A. Y(0,0) B. Y(0,0) C.Y(0.6) Y(0,0) D. Y(0,0) E. Y(0,0)

Four point masses each mass of 'm' are placed at the corners of the square of side 'a'. find the gravitational force experienced by each of the particles.

Four identical rods each mass m and length I joined to form a square. Find moment of the system about an anis passing through the center of mass of the system and perpendicular to the plane of the rods find moment of evertia about the diagonal of Also of the square.

the concentration of drug at depth x in the skin at time t after drug application, and D is the diffusion coefficient of the drug through the skin. (a) Nondimensionalise equation eqn (1).

The approximate torquespeed curve and its equation for a 14 hp shuntwound DC motor are shown in Figure P214. The rated speed for this fractional horsepower motor is 10000 rpm at a rated voltage of 130V. Determine a) The rated torque in ozin (ounceinches, the industry standard for fractional hp motors) b) The noload speed c) The operating speed

A student team is to design a humanpowered submarine for a design competition. The overall length of the prototype submarine is 4.85 m, and its student designers hope that it can travel fully submerged through water at 0.440 ms. The water is freshwater (a lake) at T 15 C. The design team builds a onefifth scale model to test in their universitys

A sample of radioactive nuclei of a certain element can decay only by emission and 3emission. If the halflife for emission is 24 minutes and that for 3emission is 36 minutes, the halflife for sample is A. 30 minutes B. 24 minutes C. 20.8 minutes D. 14.4 minutes E. 6 minutes

When the beta decay of 60Co nuclei is observed at low temperature in a magnetic field that aligns spins of the nuclei, it is found that the electrons are emitted preferentially in a direction opposite to the 60Co spin direction. Which of the following invariances is violated by this decay A. Gauge invariance B. Time invariance C. Translation

A piano tuner who wishes to tune the note D corresponding to a frequency of 73.416 hertz has tuned A4 to a frequency of 440.000 hertz. Which harmonic of D (counting the fundamental as the first harmonic) will give the lowest number of beats per second, and approximately how many beats will this be when the two notes are tuned properly A. B. C. D.

In the hydrogen spectrum, the ratio of the wavelength for Lymanradiation (n 2 to n 1) to Balmerradiation (n 3 to n 2) is A. 548 B. 527 C. 13 D. 3 E. 275

In the spectrum of Hydrogen, what is the ratio of the longest wavelength in the Lyman series (nf 1) to the longest wavelength in the Balmer series (nf 2) A. 527 B. 13 C. 49 D. 32 E. 3

A black hole is an object whose gravitational field is so strong that even light cannot escape. To what approximate radius would Earth (mass 5.98 x 1024 kilograms) have to be compressed in order to become a black hole A. 1 nm B. 1 um C. 1 cm D. 100 m E. 10 km

A current i in a circular loop of radius b produces a magnetic field. At a fixed points far from the loop, the strength of the magnetic field is proportional to which of the following combinations of i and b A. ib B. ib2 C. 126 D. ib E. ib2

The 238 U nucleus has a binding energy of about 7.6 MeV per nucleon. If the nucleus were to fission into two equal fragments, each would have a kinetic energy of just over 100 MeV. From this it can be concluded that A. 238U cannot fission spontaneously B. 238U has a large neutron excess C. nuclei near A 120 have masses greater than half that of

Which of the following nuclei has the largest binding energy per nucleon (Consider the most abundant isotope of each element.) A. Helium B. Carbon C. Iron D. Uranium E. Plutonium

Given that the binding energy of the hydrogen atom ground state is Eo 13.6 eV, the binding energy of n 2 state of positronium (positronelectron system) is A. 8E0 B. 4Eo C. Eo D. Eo4 E. Eo8

The binding energy of a heavy nucleus is about 7 million electron volts per nucleon, whereas the binding energy of a mediumweight nucleus is about 8 million electron volts per nucleon. Therefore, the total kinetic energy liberated when a heavy nucleus undergoes symmetric fission is most nearly A. 1876 MeV B.938 MeV C. 200 MeV D. 8 MeV E. 7 MeV

In the simple pendulum experiment the period T was related to the length L and the gravitational constant g via T 2T 1. Using error propagation rules, write an algebraic equation for the uncertainty T of the period T in Eq. (8), as a function of T. L. g and the errors 6L and g of the length and gravitational constant, respectively. ST 2.

The positronium atom consists of an electron and a positron bound together by their mutual Coulomb attraction and moving about their center mass, which is located halfway between them. Thus the positronium atom is somewhat analogous to a hydrogen atom. The groundstate binding energy of hydrogen is 13.6 electron volts. What is the groundstate

The solution to the Schrodinger equation for the ground state of hydrogen is 40 eran where a, is the Bohr radius and r is the distance from the origin. Which of the following is the most probable value for r A. o B. ao2 C. ao D. 200 E.

The FranckHertz experiment and related scattering experiments show that A. electrons are always scattered elastically from atoms B. electrons are never scattered elastically from atoms C. electrons of a certain energy range can be scattered inelastically, and the energy lost by electrons is discrete D. electron always lose the same energy when

If the absolute temperature of a blackbody is increased by a factor of 3, the energy radiated per second per unit area does which of the following A. Decreases by a factor of 81 B. Decreases by a factor of 9 C. Increases by a factor of 9 D. Increases by a factor of 27 E. Increases by a factor of 81

A black body at temperature T radiates energy at a power level of 10 milliwatts (mW). The same blackbody, when at a temperature 2T, radiates energy at a power level of A. 10 mW B. 20 mW C. 40 mW D. 80 mW E. 160 mW