Physics Questions and Answers October 22, 2022

For the van der pol equation VAN DER POL and the LIENARD. The van der pol system may be rewritten in state space form as (x 1)x x 0 F(x) x Oxdot F(x) uy and Ydot (iu) x Oxdot F(x) uy and Ydot ( iu)x Oxdot F(x) uy and Ydot (iu)x all of the above

6. A baseball (0.145kg) moving toward a bat has a speed of 43ms. When hit by the bat, it experiences a horizontal force as shown to the right. The force acts in the opposite direction that the ball is moving. What is the speed of the ball after it leaves the bat 10 points F(N) 20 000 15 000 10 000 5 000 0 F 18 000 N ON 3 (ms)

A column of rectangular crosssection is made of steel with Sy 380 MPa and E207 GPa and subjected to an axial compressive force P. Both ends of the column are pinpin (rounded) in Plane A, and fixedfixed in Plane B. A) Determine the ratio of (be) for equal buckling load in either plane. B) If P 15 kN and n3, determine the dimensions of the

Use the given data to determine the suitability of the electrographite steel support furnace roll, the furnace operates at a maximum temperature of 1250 degree celcius, the roll experiences heat by radiation and conduction when the stripline of 28 ton passes on it continously Find Heat transferred to the roll, the roll diameter is 160 mm and

Analyse the frame shown in figure below by slope deflection method and draw BMD and SFD. A X kNm B 1.5 El 1 El 5m 1.5 El C 3.5 m If last 2 digits of your id is 25, then take x last three digits of your id2 If last 2 digits of your id is 25, then take x last three digits of your id5 If last 2 digits of your id is 00, then take x 7.5

In a balanced 3phase circuit, a 3phase voltage source with negative phase sequence is connected to a three phase load. If the current between the C and B nodes at the load is ICB120120 Arms what is the line current I aA co Problem 1.B (8 pnts) A balanced 3phase circuit consists of a Yconnected 3phase source with negative phase sequence, a

Find the zparameters (in ohm) 211, 212, 221 and 222 of the below network with 222 221 222. Assume the value of resistor R (in ohms) 3. Z11 V1 Z11 Z12 11 (7 marks) R ww Z12 10 Q2 (6 marks) Z21 6 www (6 marks) Z22 4 12 V2 (6 marks)

A copper tube of initial diameter D80mm and 120mm in length. It is proposed operation, reducing its thickness from 10mm to 8mm. The required TNT charge weight using (12.5M) explosive forming process. Using k75000, n0.38, C390000 for TNT. (B) Dome from copper with h,1mm, D.1m, D0.75m, estimate required TNT. Using e15.4810 inlblb, 70.5, k7500,

In the following plane structure shown in Fig 1, rigid blocks are connected by linear spring. Imagine that only horizontal displacements are allowed. For this spring system, write the structure equilibrium equations K D) R in term of spring stiffness K., displacement degree of freedom u, and applied load F. Construct the element matrices and then

The solid shaft shown in Fig 2 has a diameter of 50mm and a length of 800mm. The shaft is twisted through an angle of 3 degrees at one end while the other end is fixed. Part a Calculate (a) the torque T required and (b) the maximum shear stress induced. G80GNm 12 Marks Part b To make the shaft more flexible it is to be bored along its axis.

For a graphite epoxy unidirectional lamina, following properties are available E 181 GPa, E 10.5 GPa, G 7.2 GPa and U0.02. The lamina is subjected to the following loading conditions 04 MPa, 04 MPa,T12 0 i) Compute the major poissons ratio. ii) compliance matrix for the lamina. iii) reduced stiffness matrix for the lamina. iv) strains in 12

Find i, in the circuit of Fig. 4.9 using superposition. 292 ww 4 A 392 592 wwww www Figure 4.9 For Example 4.4. 192 www 20 V 5i www 492

Let F be the function from R to R defined by F((x, y, z)) (xy, y z) Show that F is not a linear transformation. 3. Let T be the linear transformation from M,2 to the space of function from R R defined by T (a b) b) (a b) x c (You can take it as given that this actually defines a linear transformation). Determine whether the following

A ductile solid rod, of initial area (25mm) and initial gauge length (8cm), show this tabular data during simple tension process Tensile load in (N) 4220.0310 Elongation (mm) 17.7122 4317.3340 33.5254 Determine the Ludwik model coefficients of this rod numerically. 4225.6478 45.465 3957.9528 67.6031 (12.5M

Consider the reverted compound helical gear train shown with the given numbers of teeth. The normal module of Gear 1 is 3.5 mm and the normal module of Gear 3 is 5 mm. Gear 1 has lefthand helix and Gear 3 has righthand helix. The helix angle of Gear 1 is 25. The input shaft is driven at a speed of 300 rpm by a motor that delivers a power of 5 kW.

A material has a yield stress of 20 ksi, which is also the proportional limit of the material. The material is loaded axially up to 30 ksi, and then unloaded. If the material was loaded again, what would be the proportional limit of the specimen

How does quantum theory allow a rock to turn suddenly into a duck?

How does sound going slower in water make it hard to talk to someone underwater?

How high does a building have to be for a penny dropped from the top to kill a person on the ground?

How is a magnetic field just an electric field with relativity applied?

How long can you use a cell phone before getting a brain tumor?

If I hammered and flattened a penny enough, could I cover the entire earth with it?

If I'm on an elevator that breaks loose and plummets down the shaft, can I avoid harm by jumping at the last second?

A 10, 10 kVA, 460120 V, 60 Hz transformer has an efficiency of 96 when it delivers 9 kW at 0.9 power factor. This transformer is connected as an autotransformer to supply load to a 460 V circuit from a 580 V source. (a) Show the autotransformer connection. (b) Determine the maximum kVA the autotransformer can supply to the 460 V circuit. (c)

A 10, 200 kVA, 2100210 V, 60 Hz transformer has the following characteristics. The impedance of the highvoltage winding is 0.25 j1.5 2 with the lowvoltage winding shortcircuited. The admittance (i.e., inverse of impedance) of the lowvoltage winding is 0.025j0.075 mhos with the highvoltage winding opencircuited. (a) Taking the transformer rating as

A firemanstood on the middle step of a ladder directing water into a burning building. As the smoke diminished, he climbed up 4 steps and continued his work. The fire got worse, so he had to go down 8 steps. Later, he climbed up the last 9 steps and was at the top of the ladder. a. How many steps were on the ladder Show your strategy. b. If the

Consider the following two factor model for the excess returns of two stocks. 1.2F 0.4F a 0.8F1 1.6F2 eb e a e The expected return on asset A is 16 and on asset B 26. The risk free rate is 6. According to ATP framework, the expected excess returns are E re E r 1.2F 0.4F 0.8F 1.6F2 a. If the APT holds in this market, calculate the risk

Particle on a Sphere A particle starts from rest at the top of a frictionless sphere of radius R and slides on the sphere under the force of gravity. How far below its starting point does it get before flying off the sphere i.e. What does h equal to h Rh 0 R

Let E be the region in the first octant of R that lies inside the sphere x y 2 4 and above the cone z x y. (a) Set up (but do not evaluate) iterated integrals that compute the volume of E... (i) ...in Cartesian coordinates, with order of integration dx dy dz. (ii) ...in cylindrical coordinates, with order of integration dz dr do. (iii) ...in

A particle of mass m is constrained to move on the surface of a cylinder of radius R. The particle is subjected to a force directed towards the origin and is proportional to the distance of the particle from the origin. Construct the Hamiltonian function and obtain the Hamiltons equations of motion. Hint The force directed towards origin is given

Given the floor system depicted in Fig. 3.23, determine the minimum thickness of the oneway slab assuming that it is not supporting or attached to any type of construction 145 pcf and fy likely to be damaged by large deflections. Material data are we 60,000 psi.,18 x 18 in column (typical perimeter) OT 20 ft 6 in 24 ft 6 in 20 ft 6 in 24 ft 6 in

Let q, 92, ...,qn be a set of independent generalized coordinates for a system of n degrees of freedom, with a Lagrangian L(q, q, t). Suppose we transform to another set of independent coordinates S, ...,Sn by means of transformation equations qiqi(S,...,Sn, t), i1,...,n. (such a transformation is called a point transformation). Show that if the

Given the partial differential equation au(x, t) at (a) By showing all possible cases, use separable method to find the general solutions, u(x, t), of the problem. (b) Given that the boundary and initial conditions are as below Boundary conditions au(x, t) x Initial conditions u(0,t) u(1,t)0, t0 u(x,0) x(1x), 0x1. du(x, 0) at 1 u(x, t) (mm) n1

Consider the Galois field GF(24) given by Table 2.8. The element also a primitive element. Let go(X) be the lowestdegree polynomial over GF(2) that has a is B, B, B, B4 as its roots. This polynomial also generates a doubleerrorcorrecting primitive BCH code of length 15. a. Determine go(X). b. Find the paritycheck matrix for this code. c. Show

Four velocity and acceleration (25 25 50 pt) a) Write an explicit form of 4velocity defined as da ds, i.e. calculate its components and show that (120 011212) Hint Use the infinitesimal form of interval. b) Show that 4velocity u is orthogonal to 4acceleration w defined in the form of w duds. Hint The square of 4velocity equals to 1, i.e. dx

Consider the PDE xuyuy 2u, for x 0 and y 0. Using the 3step method of transformation reduce it to its canonical form, sketch its characteristic curves and obtain its general solution. 9 marks ii) Find the specific solution of the PDE studied in i) when it is subject to the Cauchy data u(x, x) 1x, for x 0. I (b) Use the method of

Using the tensor transformation F law applied to ExEy E B. B B 0 0 Ez 0 E, B E. By B 0 (1) show how the electric and magnetic field threevectors E and B transform (i.e. give explicit expressions for the primed components E, etc.) under a) a rotation about the yaxis by an angle 0, b) a Lorentz boost in the direction with parameter (or speed u

Solve the following PDE, without boundary conditions, by the method of separable variables to find all product solutions.

Solve the following PDE, without boundary conditions, by the method of separable variables to find all product solutions. 8v 25 2 T

Consider an infinite plane with a uniform positive charge density a as shown below. d The A negative point charge q with mass m is held at rest at a distance d from the sheet and released. It will then undergo oscillatory motion. What is the time period of this oscillation You may assume that the point charge can move freely though the charged

The next two questions pertain to the situation described below. a 1 d y a. 2.5 mCm b. 6.5 mcm c. 9 mCm d. 4 mCm e. 13 mCm P Two infinite conducting slabs of thickness 2.5 cm, with total surface charge densities of oa 13 mcm and ob 5 mCm are offset to the left and right each by d 0.15 m, as shown ob d 1) What is the charge density on the left

find the 1st order Correction to the energy of ground state where, H vo (a to a). 34 a

A rod PQ of proper length 1. lies along the Xaxis and moves towards the positive x direction with speed with respect to the ground (see figure), where is the speed of light in vacuum. An observer on the ground measures the positions of P and Q at different times tp and to respectively in the ground frame, and finds the difference betwen them to

The wavefunction of a free particle of mass m, con strained to move in the interval L x L, is y(x) A(L x)(L x), where A is the normalization constant. The probability that the particle will be Ino found to have the energy h 2mL2 is Ans (A) 0 pisngs 10110s (B) nilqms ovsil diod) m it Do 1 (C) 23 all yo 1515 osimy 1 (D) 18 11 110

A particle moving in a central potential is described by a wavefunction y(r) zf (r) where r (x, y, z) is the position vector of the particle and f (r) is a function of r r. If L is the total angular of the particle, the value of L2 must momentum be (A) 2 (C) 4 (B) 3 (D) 2 4

A particle of mass m and energy E 0, in one dimension is scattered by the potential shown below 21 box dr V AY x8, If the particle was moving from xo to which of the following graphs gives the best qualitative representation of the wavefunction of this particle OVE (A) P(x) (B) (x) oubo (C) Y(x) Ca (D) Y(x) V(x) a bhio b WOT VI M 0950 go a a a a

Two objects, both positively charged are on the xy plane. One object can be thought of as a point charge q located at (0, b) and the other object is a section of a ring of radius b centered at the origin with total charge q as shown in the figure. Given that the ring section is uniformly charged, find the net electric field at the origin due to

What will be the net capacitance 5.15 Mf 3.55MF Si25f III II 3.25 MF I 0.75 MF 15. OMF

Find the frequency spectrum of the periodic wave that is the periodic extension of the function f in problem 3. ,Find the frequency spectrum of the periodic wave that is the periodic extension of the function fin Problem 3. (Sketch the frequency spectrum, where y axis is Cnl)

Determine the value of the equivalent spring Constant (keq) that relates the applied force (F) to the resulting displacement (X) of the system shown below, when K 0.16. the displacement of the link to be small. Assume 4k mm m 2K mm 3K m 44 94 24 14

For the roof truss as shown answer the following questions (a) Use method of joint to determine the internal force in GE member. (b) Use method of section to determine the internal force in CD member. 400 N y 250 N A B 60 500 N C 60 30 500 N D G 10 m 500 N 30 E 30 250 N F x

The tangent offset of a point Q on a simple curve is 9.56 m. If its distance from PC along the curve is 70 m., find the radius of the curve.

A Cantilever beam with 3m span is subjected to uniform ultimate load of 100 kNm, If the beam crosssection is 550mm x 350mm (HxB) Draw shear and moment diagrams for the beam. If the maximum ultimate moment is 270 kN.m and the maximum ultimate shear is 180 KN. Calculate the longitudinal reinforcement required for the beam, perform all necessary

Given the soil conditions below, determine how high the water level could rise in Sand 2 before quick conditions, i.e., o 0, occurs at point A. Show all work to receive full marks. (Hint determine the pressure heads and total heads at A and B first) (15 marks) Datum Soil Dry sand Clay Silty clay Sand Dry Sand Clay Bulk Density (kNm) 18 19 19.5

A circular tank of 1.50 m diameter is under an internal pressure of 0.35 MPa. The lid (cover) is bolted to the tank. If the ultimate capacity of each bolt is 95 KN, how many bolts will be required to resist this pressure Use a factor of safety 2.50.

Solve each of the following simultaneous systems of equations. (a) X Y, Y X, X(0) 2, Y(0) 1. (b) X X5 Y 0, Y 4X 5 Y 0, X(0) 1, Y(0) 2.

A square plate ABCD is loaded with uniform shear forces applied along its edges. After loading point A and B are unmoved and points C and D have moved downward by 0.02 in. What is the average shear strain at point D 2 R Before loading After loading 0.02 in

Determine the moment of inertia about the x axis. Determine the moment of inertia about the y axis. y a a P Probs. 1012 b X

The flux density in the gap of a 1mA (full scale) moving coil ammeter is 0.1 Wbm2. the rectangular moving coil is 8mm wide by 1cm deep and is wound with 50turns. calculate the full scale torque which must be provided by thr springs.

please complete both of these tables TABLE 1. Pulleys Moment of Inertia, I (T) 0.200m, h 1m m (kg) (t) (s) (a) h 2(t) (ms) (a) (a)(r) (rads) Tappl m x (9.8(a)) x (r) (Nm) 0.250 m (kg) t(s) (a) h 2t 0.020 (ms) 3.070 (a) (a)(r) (rads) 0.030 2.380 Tapplmx (9.8 (a)) x (r) (Nm) TABLE 2. Pulley and TWO attached masses Moment of Inertia, 12 M (kg) RM

please complete both of these tables TABLE 1. Pulleys Moment of Inertia, I (T) 0.200m, h 1m m (kg) (t) (s) (a) h 2(t) (ms) (a) (a)(r) (rads) Tappl m x (9.8(a)) x (r) (Nm) 0.250 m (kg) t(s) (a) h 2t 0.020 (ms) 3.070 (a) (a)(r) (rads) 0.030 2.380 Tapplmx (9.8 (a)) x (r) (Nm) TABLE 2. Pulley and TWO attached masses Moment of Inertia, 12 M (kg) RM

The base current in the first transistor of the following circuit having two identical Siliconbased npn transistors of value 100, is closest to 107 51 (a) 3.6 JA 10002 (b) 0.36m4 (c) 5.0mA (d) 5.0A

What is the output voltage of the following circuit for the input current 1n4 (a) imi 10A2 1K0 99kQ (b) 11 (c) 1 (d) 1nl

In the following de A 1, Ans. 950 100. 10.0.7. Determine thee in ml. CC Iransistor circuit R0.540. R R 2kQ,R, 200 42. R 0.560 R 2000 www 10F R 2kQ ER, 240

If the temperature of air in Gabors lungs is 37 C (98.6F), and the volume is 6 L, how many moles of air n must be released by the time he reaches the surface Let the molar gas constant be given by R 8.31 J molK Express your answer in moles to three significant figures. n Submit Hints My Answers Give Up Review Part mol

State and prove the Cayley Hamilton Theorem. (You may as sume that the eigenvalues are all distinct). (b) Given A 0 1 2 3 i. Calculate et using the Cayley Hamilton Theorem ii. Calculate et using Wet W1 where W is the matrix of eigenvectors of A.

A mass M slides without friction on the roller coaster track shown in the figure. The curved sections of the track having radius of curvature R . The mass begins its descent from the height h . At some value of h , the mass will begin to lose contact with the track . Calculate the minimum value of h for which this the mass lose the contact with

A mass M slides without friction on the roller coaster track shown in the figure. The curved sections of the track having radius of curvature R . The mass begins its descent from the height h . At some value of h , the mass will begin to lose contact with the track . Calculate the minimum value of h for which this the mass lose the contact with

In the above 10 ohm resistor, What is current 21 V Lum 502 502 1002 In the above 10 ohm resistor, What is current 0.60 A 3.0 A 1.2 A 24A 502

A conducting sphere of radius R is placed in a uniform electric field E, directed along axis. The electric potential for outside points is given by z VE (1(Rr))r cose, where r is the distance from the center and is the polar angle. The charge density on the surface of the sphere is (a) 3 E cos 0 (b) E E cos (c) 3, E cos 0 (d), E cos

A stationary boat in the ocean is experiencing waves from a storm. The waves move at 52 km/h and have a wavelength of 145 mm . The boat is at the crest of a wave. How much time elapses until the boat is first at the trough of a wave?

A point charge is kept d distance above an infinite conducting plane. What is the energy stored in the configuration (n) 1 q 47 , 2d Ans, 10 (b) Solution. (b) 1 g 4 En Ad (c) 4, E 2d (d) 4 E 4d

The value of the integral is (a) 12a (b) 12 1 00 J 00 COS X x a (c) exp() (d) exp(a)a

The electron of a free hydrogen atom is initially in a state with quantum numbers n 3 and 2. It then makes an electric dipole transition to a lower energy state. Which one of the given states could it be in after the transition (a) 11 2, (c) n 3, f 1 P 0 (b) (d) 12 2, n 3, 2 l 1

Consider a monatomic solid lattice at a low temperature T To, where To is the characteristic Debye temperature of the solid (Th homky where om is the maximum possible frequency of the lattice vibrations). The heat capacity of the solid is proportional to (a) TTp (b) (TT) (c) TDT (d) (TDT)

A plane electromagnetic wave, which has an electric field E(X, t) (P Q) exp iw (1) is passing through vacuum. Here P, Q and w are all constants, while c is the speed of light in vacuo. What is the average energy flux per unit time (in S1 units) crossing a unit area placed normal to the direction of propagation of this wave, in terms of the above

The state ) of a spin1 particle is given by 1 4) 3 (11,1) 2i 3 in 1,0) exp 1,1) exp. 3 where S, Mg) denote the spin eigenstates with eigenvalues hS(S 1) and hM, respectively. Find (S), i.e. the expectation value of the x component of the spin.

A particle of mass m moves in a twodimensional space (x, y) under the influence of a Hamiltonian 1 H (p p) mw (5x 5y 0. 6xy) 1 2772 Find the ground state energy of this particle in a quantummechanical treatment.

Define ( ), and o, i( ), where the o are Pauli spin matrices and f,f obey anticommutation relations f, f0,f, f1. Then o is given by (a) ff1 (b) 2ff1 (c) 2 f f 1 (d) f f

Consider a threestate system with energies E, E and E3g (where g is a constant) and 1 1 and 3) 00 6 respective eigenstates y) If the system is initially (at t 0), in state ) (a) 0 1 what is the probability that at a later time t system will be in state y,) 0 3gt 2 c) cos (3 4 (b) sin 3gt 2 E3gt 2 1 4 (d) sin(1

In a rough approximation of a baseball game assume the game ends after each team gets 27 outs. So far during the 2022 MLB season, the median number of strikeouts during a game for a team is roughly 9. Let X be the random variable representing the number of strikeouts a team gets per game. Lets model the number of strikeouts per game, X, using the

Classify the following secondorder partial differential equations. 1.2 X0 1.3 1.4

The electrostatic charge density p(r) corresponding to the potential 19 1 ( 1 7) exp(ar) 4TE 2 is p (a) q8(r)2qa exp(ar) (c) q8(r)qexp(ar) 2 (1) (b) q8(r)q. exp(ar) (d) q8(r) 2qa exp(ar)

What value the following infinite series will converge to (A) 126 (B) 12 (C) 3 (D) 6 n1 2 2n

Use the power rule to differentiate each of the following functions a. h(t) 180 16t 4.9t b. V(r)r c. f(t) 1 t 12 1 d. f(x)

A simply supported beam span L and flexural rigidity El carries two equal concentrated loads at each of the quarter span points. Using Rayleigh Ritz method, determine the deflection under two loads. L4 P X D L4 B

For the differential amplifier circuit given below, derive an expression for the gain defined as Ad Vodvid. Assume that the two transistors Q and Q are identical. VBE Vid 2 Rc Vol Q Q VodV02 REE Vcc VEE Rc VBE Vid 2

There is a square of infinite length and width a. Some of its portion is cut. Refer to the figure given below V(x) A a bchd Vo gnhi Vo f k Evaluate bcdefghijklmnpq 18 1 st The segment OA is a straight line. The energy of first three states for the above (using 1 order perturbation theory) are and X lum hn Vo q

Suppose a spherically symmetric liquid planet of radius R is in hydrostatic equilibrium has a density profile given by p(r) po(1ar) if r R and O if if r R where pO 0 and 0 a 1 are constants. a) Let M M(r) denote the mass of material enclosed by radius M(r) 4pOr3 ( (13) (ar4R)) if r Rand 4r3 ((13) (a4)) b) Assume that the planet is in

Use Matrix Method to obtain an expression for focal length of a Coqxial Combination of two thin lenses having local lengths f1 and f2 Separated by distance a/(t)

What are the implications of the uncertainty principle on the measurement of quantum systems?

Calculate the number of electric lines of force originating from a charge of Ic

In the following figure, if A 100,000, r 2 MC2 and r 750, what are the closed loop input and output impedances If the opamp has lin(bias) 80 nA, lin 20 nA, and V in (off) m(off) voltage X Vin 1 ww rin (CL) 15 V 15 V Tout (CL) 100 kQ 2x. What is the output offset 100 kQ 2 k

Measurement Physics Quiz. Question 1. : What is the principle of a digital multimeter (DMM)? A) It uses a needle to indicate the measurement on a dial B) It uses an analog-to-digital converter (ADC) to convert the measurement to a digital display C) It measures only DC voltage D) It cannot measure resistance Question 2. What is the SI unit of

Ex A strain gauge having a resistance of 120 W and a gauge factor of 2 is subjected to a stra Find the expression for the change in output voltage when the strain gauge is connect in ballast circuit having a ballast resistance of 12092 and an input voltage of 6V. of (2010 sin 314 t) x 106 (a) (b) If a capacitor is connected in one of the output

A metallic spherical shell has on inner A charge Q Vading R and outer radius R is placed at the centre of the Spherical cavity. What will be surface charge density on (i) the inner surface ) the outer Surface

If the force acting on a point charge kept on the axis of an electric dipole is F, what will be the amount of force if the distance of the point charge is doubled from the dipole a) 2F b) F8 c) F2 d) F4

For the figure below (assume Vio1.2mV IB60nA I8nA) i. Determine Voor due to input offset voltage and input bias current. ii. Determine offset minimizing resistance, RoM. iii. Determine Voor after connecting offset minimizing resistance, ROM 0 R1 ww 1.0k IF 3 Rf www 5.1k U1 OPAMP3TVIRTUAL

The 714C is configured as a noninverting amplifier. The following data are given for the circuit A400,000 R47002 R33MQ R4.7kO R6002 Supply voltage15V Maximum output voltage swing13V Unity gain bandwidth0.6MHz Compute the closed loop parameters AF, RF, RF, fr and Voor

Define PSRR. For AF771op-amp, PSRR = 70dB minimum, what is the numerical value of the PSRR?

Design an integrator to integrate the signal in the frequency range of 1KHz to 20 KHz. Sketch the output for the sine wave of frequency of (a) 100Hz and (b) 10KHz