Physics Questions and Answers July 21, 2020

Consider a particle of mass m moving in one dimension under the influence of a constant gravitational acceleration g. Then the corresponding potential energy is given by V(x) mgx and the Lagrangian of the mechanical system becomes L(x,x) mi mgx Like the free particle and the harmonic oscillator cases, this model can be solved exactly. (a) Solve

Determine the energy levels (E 0) for a particle moving in a field of potential energy V(x) A (e 2 ex) (P.M. Morse). (Hint Schroedingers equation is dy 2m EAe2ax 2 Aeaxy 0. dx We introduce a new variable y 2ax n 22m A ah and the notation so that 2mE 2mA (1). Write Schroedingers equation in the new form. ah a Find the necessary conditions of

A multiloop circuit is given below. Some circuit quantities are not labeled. It is not necessary to solve the entire circuit. (a) What is the potential difference VVa Be careful with the sign. (b) What is the direction of the current 6.0 V E de 11 Q2 w 0.6 A M 19 19 02 W 0.4 A through the battery labeled as E b 15 Q2 0,3 A 13 Q2 M M 2102 30 w 25

One mole of hydrogen gas and 2 mole of helium gas are mixed in a container and maintained at a fixed temperature T. How does the total pressure P exerted by the hydrogen molecules compare to the total pressure PHe exerted by the helium molecules Note that a molecule (atom) of hellum has twice the mass of an H molecule. OPH2PHe OPH 2 PHe OPHPHe O

The transverse displacement, y, of a taut string from its equilibrium position at some point, x, and time, t, is given by y(x,t). By appropriate differentiation, show that the wavefunction y(x,t) = f (x/x0 + t/t0) is a solution of the wave equation for all functions, f , and derive an expression relating the constants x0 and t0 to the wave speed.

For the two cantilever beams whose free ends are connected to springs shown below, give the expressions for the spring constants ki and k2 in term of the Youngs modulus E1,2, length L1,2, and area moment of inertia 1,2, and determine the equivalent constant keq for the system. 4 k Ez. 1 2. E.1

A desperate hiker has to think fast to help his friend who has fallen below him. Quickly, he ties a rope to a rock m r = 402 kg and makes his way over the ledge (see figure). If the coefficient of static friction between the rock and ground is s = 0.322, and the mass of the hiker is h =74.9 kg, what is the maximum mass of the friend, m f ,that

m Number kg

What is i if light hits glass (n = 1.56) so that it completely polarizes when reflected? A light ray travels from glass to air at i=35. What is the light speed in the glass (n=1.6)? A light ray travels from glass to air at i=35. What is for total internal reflection?

Deserts in the North America occur where erosion has reduced the landscape to isolated, small mountains surrounded by broad sedimentfilled basins. continental interior locations in the rain shadow of major mountains. air is sinking around the Tropic of Capricorn. landscapes are flat. Submit Part B Request Answer Erosionaldepositional processes

Red laser light (X6.5 x 107 meters) goes straight through a double slit and onto a wall behind the double slit. The distance between the double slit. and the wall is 6 meters. The slit spacing is 7 x 10.5 meters. What is the distance between the 1st bright fringe and the central maximum Type in your answer in meters to the 3rd decimal place.

Consider a very long solid cylinder of radius R with nonuniform charge density given by p(r) ar. This cylinder is surrounded by a cylindrical conductor of inner radius R and outer radius R. Find the potential difference V (2R) V(0). Law Application overhead view R

A 2.0 kg box is held in place against a wall with a force, Fas applied to it, as shown below. 21.3N The coefficients of friction between the block and the wall are 0.50 and 0.30, respectively. Determine the magnitude of the smallest force that can be applied to prevent the box from sliding. 9.24N 36.0N 55.4N 2.0 kg 18.5 N 45

Using 1. the number of stars in the galaxy (N) 2. the age of the Galaxy (TG) 3. the fraction of stars with planets (fp) 4. the number of environments per star that could possibly support life (ne) QUESTION 1A.) FROM the drake Equation Provide estimates for each of the four items listed above to be the best known in the Drake equation, and

A cylindrical glass tank with a diameter of 8.6 cm and a height of 25 cm is inverted and inserted into another tank of water. If no air is allowed to escape from the glass container when submerged, what is the height of the air column in the glass tank when its edge is nem below the surface of the water?

Calculate the components of a four-vector A and the scalar product of the four-vectors A^ and B^ where (a) A^ = (A^t , A^x , A^y , A^z ) and B^ = (B^t , B^x , B^y , B^z ) in Minkowski space defined by the line element ds2 = dt^2 + dx^2 + dy^2 + dz^2 . (b) A^ = (A^t , A^r , A^ , A^ ) and B^ = (B^t , B^r , B^ , B^ ) in Minkowski space defined by the

A 50 kg cannonball hits a 12,000 kg tank that is initially at rest. The cannonball embeds into the tank, and both move at the same velocity for 50 cm until coming to rest. The coefficient of friction between the tank and the pavement is 0.45. A. How much work does friction do on the system? B. What is the velocity of the system right after the

Each of the following equations was given by a student during an examination Here mmass, v speed, vospeed, g, and an acceleration, ttime, hheight 1) mv mv mgh 2) v v at 3) ma v Do a dimensional analysis of each equation, find the correct answer which is given below. A) Equation 1 B) Equation 3 C) Equations 1 and 2 D) Equations 1 and 3. E)

For an ideal gas, the specific heat at constant pressure Cp is greater than the specific heat at constant volume Cv because the O A. pressure of the gas remains constant when its temperature remains constant O B. gas does work on its environment when its pressure remains constant while its temperature is in creased C. increase in the gass internal

Two masses m1 and m2 are connected in the manner shown: The system is accelerating downward with acceleration of magnitudeg/2. a. Determine T2. b. Determine T1.

T1 m1 m2 T2 a g2

Two blocks are connected by a lightweight string passing over a pulley, as shown in the figure below. The block with mass m 17.5 kg on the incline plane accelerates up the plane with negligible friction. The blocks acceleration is a 1.40 ms, and the tension in the segment of string attached to this block is T. The hanging block has a mass of m

Lions can run at speeds up to approximately 80.0 kmh. A hungry 108 kg lion running northward at top speed attacks and holds onto a 35.5 kg Thomsons gazelle running eastward at 75.0 kmh. Find the final speed ty of the liongazelle system just after the lion attacks. t Find the angle between the final velocity of the liongazelle system and the East

The object shown in the figure below consists of a thin rod of length 22.5 cm and mass m 1.20 kg with a solid ball of diameter d 10.0 cm and mass M 2.00 kg attached to its top. The object is free to pivot about a frictionless axle through the bottom of the rod. The object is initially vertical and at rest when it starts to rotate clockwise. M

Climate change has caused many changes on earth already. According to the videos in week 4, which of the following are attributed to climate change Select all that apply. sea level rise ocean acidification agricultural land shifts and growing food is becoming more difficult increase in global surface temperatures health effects such as asthma,

Captain Kirk is chasing a Gorn and sees the Gorn will reach safety in 250m, as measured from Kirks location. Kirk is running at 5 ms while the Gorn is running at 4 ms and the Gorn has a 90m head start. Scotty brings the transporter back online and can transport Kirk instantly to catch the Gorn. How far must Kirk be transported to catch the Gorn

A hawk with mass m 1.9 kg is diving at a speed vn xaxis. A pigeon with mass mp The hawk catches the pigeon and holds onto it. m 24 at an angle of 60 below the S 0.52 kg is flying in the xdirection at a speed vp 9.4 A. Draw a quick sketch of the initial setup, and use it to find the components of the initial momentum of the system of the hawk

The magnetic field strength of the Earth is 0.60 mT at the magnetic North Pole on the Earths surface. If the magnetic field can be modeled as a permanent magnet a the center of the earth (the NiFe inner core) surrounded by a current loop with a radius equal to 0.2RE. For simplicity, assume that each contributes half of the field measured at the

Metal A has a density of 5 gcm3 and metal B has a density of 3 gcm3. 1200 g of metal A and 600 g of metal B are melted and mixed and then recast into a block. a) What is the volume of the block b) What is the density of the block

Two blocks are attached by light wires in the configuration shown in the figure below. The block B of mass 70.0 kg rests on a wedge platform fixed to the floor, and the static coefficient of friction between the block and the wedge surface is 0.24. Find the maximum mass of block A for which the block B will remain at rest. B 30 Wedge fixed to

15 marks Many fish and other aquatic animals can detect electric fields. A famous example is sharks whose sensitivity to electric fields is sufficient to detect the EMF induced in their body as they move through the Earths magnetic field. The electrically sensitive part of the shark is known as the ampullary organ. We can think of the ampullary

The diagram below shows a dipole centered at the origin and along the xaxis. Determine an expression for the total electric field at a point A (r 3.7L,0) in terms of q and L. Calculate the magnitude of the total electric field at A, when q 6.45x107 Cland L 43.8 cm (L,0) 9 O (L,0) q (r,0) A Submit Answer Incorrect. Tries 17 Previous Tries

A 60 kg skydiver dives straight down like an arrow. They can be treated as a streamlined body with a drag coefficient of 0.4 and a circular cross sectional area with a radius of 20 cm. The density of air is about 1.204 kgm. They pull their parachute tags and the parachute is a hollow hemisphere with a drag coefficient of 1.42 and a circular cross

Express the vector in terms of a, b, c vectors. A) a bc B) a b c c) abc D) ( a b c) E) abc P

A box with an unknown mass is hanging from two ropes as shown to the right. If the tension in each rope is 73.5 Newtons, calculate the mass of the box. Tension in each rope 73.5N

Two bugs sit on an oldfashioned record, as shown in the figure. Bug 1 is halfway between bug 2 and the axis of rotation. What is the centripetal acceleration of bug 1 O One quarter bug 2s centripetal acceleration. Twice bug 2s centripetal acceleration. Four times bug 2s centripetal acceleration. One half bug 2s centripetal acceleration.

(a) A pilot will black out if her acceleration exceeds a limit (typically 5 gees). We dont want that on our space rockets If the engines are firing at max burn rate and exhaust velocity, will she experience higher, or lower, acceleration as her journey proceeds Or, when the engines are firing, is this a constant acceleration situation (b) Write a

Spaulding Classification The Spaulding classification scheme was devised as a logical way to determine the disinfection schemes required for items used during patient care. Despite being over half a century old, it remains the clearest and most concise way of assessing an object's infection risk. This is important as it ensures all items receive

Calculate the angle of incline of an oak board on which a person of weight W can stand without sliding down. Hs0.6 5 Standing on an incline. F

A pyrotechnician releases a 3 kg firecracker from rest. At t 0.4 s the firecracker is moving downward with speed 4, when it begins to explode into two pieces with masses m top 1 kg and mbottom 2 kg. At the end of the explosion (t 0.8 s), the top piece is moving S upward with speed 4 m S A. What is the magnitude and direction of the total

988 A particle of mass m 1.0 kg, traveling at speed vo 10 ms, strikes a particle at rest of mass M 4.0 kg, and rebounds in the direction from which it came, with a speed v. If the amount of heat produced in this collision is 20 J, find vr. (Define all the quantities you introduce in a sketch, and state clearly from what physical laws your

(a) B (b) HONI 2r Path 2 220.092 Path 1, TRO showexplain that the toroidal solenoids magnetic field of path 1 and path 3 is equal to O and show how the magnetic field of path 2 is Path 3

Find nonzero scalars a, B such that for all vectors a and b, in the given equation. a(a 2b)Ba (4ba0 A) a2 B1 B) a2 B3 C) a 1 B3 D) a2 B3 E) a2 B3

In the xy plane a point P(21) is given. Find its polar angle in radians. A) 0.4630 B) 3.605 C) 2.677 D) 0.463 E) 2.677

A reflection grating spectrograph with a 0.2 mm by 4.0 mm slit is at the focal plane of a 4.0-meter diameter telescope. a) What is the focal length of the telescope if this slit has a size of 1.0 arcsec by 20.0 arcsec on the plane of the sky?

A boat sails 5 km southeast then 3 km due west. Approximately how far from its starting position is it now A) 8 B) 2 C) 4 D) 5.8 E) 3.6

Determine the magnitude of the resultant force of the three forces which are shown in the figure. E A) 29.7 N B) 54.2 N C) 90.8 N 24.0 N D) E) 75 N F50 N F50 N F75 N

Calculate the vector cross product ax b when a 3 2k and b 4 . A) 21817k B) 2 8j 7k C) D) E) 2 8j 7k 4 2k 412k

7. An infinitely large plate with a thickness dcarries a current with a density Jalong the zdirection. The crosssection of the plate is given in the figures below, with the x, y, z coordinates. (a) 7 When the current density is positive and uniform, 6 (0), find the direction and magnitude of the magnetic field for the region x magnitude of the

A 4.3 kg block located on a horizontal floor is pulled by a cord that exerts a force F 10.5 N at an angle theta 40 degrees above the horizontal, as shown. The floor has a coefficient of kinetic friction uk 0.1. Determine the accelaration of the block in ms Sum all forces in the horizontal direction T1Rx F1S Fnet,y Then use Newtons Second Law

7.2 The lens with a focal lengths of 80.0 cm and mirror with a focal lengths of 50.0 cm are separated by 1.00 m as shown in Figure 6. If an object is placed 1.00 m to the left of the lens, (a) Locate the final image. (6) (b) State whether the image is upright or inverted, Object Lens 1. 1.00 m 1.00 m Mirror (1)

A 2.50 litres of boiling water (100 C) is poured into a 0.650 kg glass bowl that was initially at 837 J.kg.K 24.0 C. Cw4186 J.kg. K and cg 1 (a) Calculate the temperature at which thermal equilibrium is reached. Ignore other heat flows. (6) (b) The combination is then allowed to cool off, back to 24.0 C. Calculate the total amount of (4) heat

15 marks Consider a model of a spherical cell of radius r. The interior of the cell we will model as a conducting sphere of radius ra. This is separated by a lipid layer of thickness a and dielectric constant K from the exterior of the cell which we will also model as a perfect conductor. The interior of the cell is negatively charged. With these

A 27 gallon steel container is completely filled with carbon tetrachloride. Its temper ature is 7C. The average volume coeffi cient of expansion for carbon tetrachloride is 0.000581(C). How much carbon tetrachloride will spill over when the temperature rises to 26C As sume that the steel container is held at con stant temperature so that its

Each of the following equations was given by a student during an examination Here mmass, v speed, vospeed, g, and an acceleration, ttime, hheight 1) mv mv mgh 2) vv at 3) ma v Do a dimensional analysis of each equation, find the correct answer which is given below. A) Equation 1 B) Equation 3. C) Equations 1 and 2 D) Equations 1 and 3 E)

Write down the expressions for reflection and transmission coefficients for both TE and TM cases when the incidence angle is 0. Calculate the values for and airglass interface when nair 1.00 and nglass 1.50 Similarly, write down expressions for reflectance and transmittance values at normal incidence. Verify the that the reflectance at the above

Determine the directions of the following unknowns choices up, down, left, right, into the page, out of the page 1) F 2) m 3) B 4) B at center of arc Note The loops and the arc lie along the plane of the page di

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can have a meaningful quantity A) (PQ)R B) PQR C) PQR D) (PQQ)R E) (RQ)R

Discuss three contributions of the early Greeks to environmental health. Review and summarize an article on environmental health that you have seen in a newspaper during the past week. Share how the issue discussed in the article is/or is not relevant to the community in which you live. Be sure to provide an APA Citation or URL of the article that

6. A cross section of an infinitely long, conducting cylindrical wire of radius R is as shown in the figure (A). The wire carries a current of uniform density in the positive zdirection. R X R R (B) x (A) (a) 7 Find the direction and magnitude of the magnetic field for the region Rand r R, and draw the graph of the magnitude of the field vs r,

On devices like your smartphone, there is a small camera. Your smartphone is very thin, so the lens must be very small and the distance between the lens and screen of this camera is very short. To make sure you can create images on this screen a short distance away, the lens a) must have a short focal distance, so the index of refraction should be

Each of the following equations was given by a student during an examination Here mmass, v speed, vospeed, g, and an acceleration, ttime, hheight 1) mv mv mgh 2) v v. at 3) ma v Do a dimensional analysis of each equation, find the correct answer which is given below. A) Equation 1 B) Equation 3 C) Equations 1 and 2 D) Equations 1 and 3. E)

The terminal velocity of a copper ball of radius 2 mm falling through a tank of oil is 6.5 cms. Find the viscosity coefficient of the oil if density of oil 5103 kgm3 and density of copper is 9103 kgm3.

Consider water flows at a velocity u over a flat plate of length L (shown below). Assume that transition from laminar to turbulent flow occurs at a point on the plate atx. The temperature of the flow outside the boundary layer is T, and the plate is at temperature T.. The following equations can be used to calculate the Nusselt number of laminar

We know that a particle performs a SHM and that at instant t1 = 10 s its position, velocity and acceleration are respectively equal to x1 = 5.8438 mm, v1 = 61.199 mm/s and a1 = 11834 mm/s 2 . Determine: (a) What is the period of the motion? (b) Find the equation x(t) of motion. (c) At what time t2, immediately after 20 s, will it be back at x1

A gas can be described by the following equation of state P RT (vb) where b 5 E4 m3mol and cp(ig)35 Jmolk. (a) Develop an expression for cp(real) for this gas. (b) One mole of this gas flows through an adiabatic porous plug. It enters at 10 bar, 300 C and it exits at 1 bar. What is the exit temperature (d) What is the entropy change of the

A sphere of solid substance having a radius of 4 mm is suspended in a large volume of gas at 350 K and 0.98 bar. The percentage volume of that substance at the surface is 60% and at 4 mm around the substance is 5 %. The diffusivity of gas of that substance in the gas occupied it at 318 K, 420 K and 500 K is 2 10 -6 m 2 /s, 3 10 -6 m 2 /s, 5 10

A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s2 until its engines stop at an altitude of 150 m. (a) What is the maximum height reached by the rocket? (b) How long after lift-off does the rocket reach its maximum height? (c) How long is the rocket in the

Problem 1. (Review of the wave equation) The onedimensional wave equation is a partial differential equation and in Cartesian coordinates is given by x v dt where is the y(x,t) is the wave function. To solve the equation we let y(x,t) X(x)T(t) and substitute into the partial differential equation. (a) Show that substituting y(x,t) X(x)T(t) into

The wellmixed bubbler tank is used to carbonate water. The tank has a volume of 2 m and a diameter of 1 m. The process operates at steady state. Pure water (no CO) flows continuously into the tank at a rate of 0.45 mmin (25 kgmole H0min) and carbonated water (containing dissolved CO) continuously exits the tank. Pure CO enters the tank through a

5. Amdahls Law For an important application, an old processor spends 30 of its time on executing Jtype instructions, 40 of the time on executing Rtype instructions, and 30 of the time on executing Itype instructions. a) 10 points An engineer claims it is possible to redesign the processor to achieve 2X speedup simply by speeding up one (and just

A. What is the shortest time that a jet pilot starting from rest can take to reach Mach-3.4 (four times the speed of sound) without graying out? (Use 331m/s for the speed of sound in cold air.) This is what I did but I keep getting it wrong: a=4g=4(9.81m/s^2)=29.43m/s^2 v=4 x 331m/s=1324 m/s then used equation: to solve for t which yields: y= B.

v v at Vo

The rate of the reaction, A+BPis3.6102 mol dm3s1 when [A] = 0.2 moles dm3 and [B] = 0.1 moles dm3 . Calculate the rate constant if the reaction is first order in A and second order in B.

Pressure data obtained from a constantrate drawdown test run on an oil well are shown in the table below. Estimate formation permeability, skin factor, pressure drop due to skin, reservoir pore volume and flow efficiency knowing that 9 260 stbd 0.1 Mo 0.75 cp h 65 ft Time, hr 0 1.62 3.44 4.29 5.51 6.32 7.28 8.44 10.82 11.49 15.9 18.8 22.2

PGE 437 Assignment The data in the below table is recorded during a constant rate pressure drawdown test. Determine a) formation permeability b) skin factor c) additional pressure drop due to the skin d) the pore volume of reservoir drained in barrels a13 cp B1.73 rbblSTB r.0.25 ft 0.186 h8 ft q115 STBD c1410 1psi Time (hours) 0.00 0.10 0.15 0.20

The figure below shows three small, positively charged spheres at three corners of a rectangle. The particle at upper left has a charge q 6.00 nC, the one at the lower left has a charge of q 5.00 nC, and the one at lower right has a charge q 8.00 nC. The rectangles horizontal side has length x 5.00 cm and its vertical side has length y 2.50

An experiment was performed to test the effect of three process variables on the deviation in filling bottles with a certain soft drink up to the specified height. The variables investigated are percent carbonation, operating pressure in the filter, and the line speed. 16 Experiments were performed and the data can be found in the file

carbonation, pressure, linespeed,deviation 10,25,200,1 12,30,200,2 12,25,200,1 10,30,200,0 12,30,250,6 10,30,250,1 12,25,250,1 12,30,250,5 12,25,200,0 10,25,250,1 10,30,250,1 12,25,250,2 10,30,200,1 10,25,200,3 12,30,200,3 10,25,250,0

This is based on your personal story, so the only references should be limited to the cultural evaluation models we studied in class (Hofstede, Lewis, Meyers) You see, we cannot draw lines and compartments and refuse to budge beyond them. He paused, considering what he had just said. 'Yes', he repeated. 'In the end, it's all a question of balance.

A refrigeration system using refrigerant 22 is to have a refrigerating capacity of 80kW. The cycle is a single-stage vapor compression cycle(Rankine cycle) in which the evaporating temperature is -8 o C and the condensing temperature 42o C. a) Determine the volume flow of refrigerant measured in cubic meters per second at the inlet to the

An assembly process consists of three tasks: Task#1, Task#2, and Task#3. It takes 2 minutes to complete Task#1, 5 minutes to complete Task#2, and 3 minutes to complete Task#3. The product is assembled in an assembly line with three workers and each worker performs only one task. Estimate the Throughput Rate (per hour) for this assembly process in

A well-type solid-state (or scintillation) detector allows for the increase in what property? a) worker efficiency b) quantum efficiency c) scintillation efficiency d) counting efficiency

Draw various parts of the Kenter lugless shackle. Show how the joining shackle is used in joining the 4th shackle and how they are marked to facilitate identification.

In addition to the financial statements, including the accompanying Notes, the Corporate Annual Report of a publiclytraded company includes all of the following sections, except Management Discussion and Analysis Report on Internal Control Report on Faimess of the Financial Statements All of the above are included in the Corporate Annual Report

Short Bakers makes baked goods for catered events and for sale at local grocery stores. The owner of Short Bakers believes that a new type of breakfast pastry would sell well for a price of 21.00 per dozen. Short estimates unit materials costs to be 4.85 for the pastry, and overhead costs would average 1.15 per dozen. The local wage rate for

A strange quark, strange and strange quark come together to form a particle. What is the spin of this particle? What is the charge of this particle? What is the baryon number of this particle? What is the strangeness of this particle? What is the charm of this particle? What is the bottomness of this particle? What is the topness of this particle?

Consider the given circuit, where is 3emA. The voltage vo(t) is equal to 1.6 et microV. What is L in H is Vo eq i L ell ell 12 4 mH 6 mH

Consider a particle of mass m in 1D described by the HamiltonianHp22ma(pxxp) Bx2, where a and are real constants,p is the momentum, and x is the coordinate of the particle.(a) For what values of a and this Hamiltonian is bound from below (b)Find the eigenvalues of H.

Q1 a) Express the vector field H xyz ax xyz ay xyz az in cylindrical coordinate and determine H at (3,4, 5) b) Let A 2xy ax xz ayy az. Evaluate A dv over a cylindrical region p 3,0 z5 c) Evaluate the divergence and curl for the given vector F pz cost ap zsin az d) If F x ax y ay (2 1) az, find J. F.ds, where S is defined by p 2, 0

In the summer holiday, each student is required to write at least one book report one book report. The following table represents the probability distribution function of the number of book reports (X) a student has written in the summer holiday. x 1 2 3 4 5 P(X=x) 0.8k k 0.35 0.15 0.05 (a) What is the value of k? (b) Find E(X) and (X) (c) Suppose

How far from a convex mirror must a pencil be held to form an image of half 1 pencil size the radius of the mirror is 40 cm.

If the momentum of an electron is changed by Ap, then the deBroglie wavelength associated with it changes by 0.50. The initial momentum of the electron will be Ap Ap 199 3) 199 Ap 4) 400 200 1) 2)

Estimate the heat loss by natural convection from the surface of a thin vertical plate that is maintained at a temperature of 1250C. The dimensions of the plate is 0.5 m x 100 mm. The plate is exposed to still ambient air temperature of 25C. From experiments, it is observed that the correlation Nu (GrPr) 0.33 hold for all types of flow behavior.

1. Find V(x,0) for a Gaussian wavepacket (k) Aea (kko) where A is a normalization factor to be found. Calculate the probability of finding the particle in the region a2 x a2. 2. Find o(k) for a square wavepacket V(x) Aeikoz 0 xa x a Find the factor A so that (r) is normalized. Hint Use Fourier Transform to solve above two questions. (1) 3. A

2. Relativistic charged particle Consider the action of a (relativistic) charged particle coupled to a background gauge field, A. living in Minkowski space. It is governed by the action S2 ds (me do (mc A (z (0)) (G).) where (a) General covariance in one dimension. Suppose we reparametrize the worldline according to 53(s). Use the chain rule to

In a common-base connection, the emitter current is 6.28mA and the collector current is 6.20mA. Find the common base DC current gain.

Two flask of equal volume have been joined by a narrow tube of negligible volume. Initially both flasks are at 300K containing 0.60 mole of O gas at 0.5atm pressure. One of the flask is then placed in a thermostat at 600K. Calculate final pressure and the number of O gas in each flask.

In the below circuit, determine the phase angle between the applied voltage and the current at the second critical frequency f2 (i.e. f2 fr BW2). R 50, L 7 H, C 17 nF, and Vs 7 V and 0 phase If the current is leading the angle should be positive and if the voltage is leading the angle should be negative. The result should be in degrees.

ML Find the marked angle change 0 and 0 for a moment M. 0 Enter the constant K length L, bending stiffness EI. Example if you think 0 ML (8 EI), then enter 8. 0 0 3 0 ML Find the marked angle change 0 for a moment M. 0 length L, bending stiffness EI M M Enter the constant K For your information. These answers are called flexibility

A (6 m) long pipe is inclined at an angle of 20 with the horizontal. The smaller section of the pipe which is at lower level is of (100 mm) diameter and the larger section of the pipe is of (300 mm) diameter as shown in Fig. bellow. If the pipe is uniformly tapering and the velocity of water at the smaller section is (1.8 ms), determine the

Reproduce equation (3.23), (3.24) & (3.25) by using equation (3.22). ds^2=dr^2+r^2 d^2 (3.22)

rr g(argrp Orgpr Opgrr) rr 29 (Orgrr Orgrr Orgrr) gro (ar gre argor degrr) (1)(00 (1) (00 0)(0) (0 00) (0) (000) ONIH 0. 61 (3.23)

A 100 m diameter wind turbine drives an induction generator at a fixed speed through a gearbox of ratio 192. The induction generator is connected to a 20 kV, 50 Hz grid at the point of common coupling (PCC) via a transformer and an overhead line. The transformer rating is 3 MVA with a rated voltage of 0.96 kV on the LV side and 20 kV on the HV

the same rate r(a, 3) is (1 parameter.) Show that the sum of two independent Gamma distributed random variables with parameter 3 is Gamma distributed. You can assume that the c.f. of distribution it3). (The parameter a is called the shape parameter, and 3 is called he rate