Physics Questions and Answers September 25, 2022

The primary source of the suns energy is a series of thermonuclear reactions in which the energy produces is c times the mass difference between A. two hydrogen atoms and one helium atom B. four hydrogen atoms and one helium atom C. six hydrogen atoms and two helium atoms D. three helium atoms and one carbon atom E. two hydrogen atoms plus two

The energy required to remove both electrons from the Helium atom in its ground state is 79.0 eV. How much energy is required to ionize Helium (i.e. to remove one electron) A. 24.6 eV B. 39.5 eV C. 51.8 eV D. 54.4 eV E. 65.4 eV

The ground state electron configuration for phosphorus, which has 15 electrons, is A. 15 25 2p6 35 3p B. 15 25 2p6 3s 3p 3s 3d C. 15 25 2p6 152, 3s 3d4 D. 282 E. 15 25 2p 3p3d

A wire of diameter 0.02 meter contains 1028 free electrons per cubic meter. For an electric current of 100 amperes, the drift velocity for free electrons in the wire is most nearly A. 0.6 x 1 B. 1x 109 ms 10 ms C. 5 x 1010 D. 2 x 104 ms E. 8 x 10 ms x 1029 ms

A 5 kilogram stone is dropped on a nail and drives the nail 0.025 meter into a piece of wood. If stone is moving at 10 meters per second when it hits the nail, the average force exerted on the nail by the stone while the nail is going into the wood is most nearly A. 10 N B. 100 N C. 1000 N D. 10,000 N E. 100,000 N

A 2kilogram box hangs by a massless rope from a ceiling. A force slowly pulls the box horizontally to the side until the horizontal force is 10 Newtons. The box is then in equilibrium as shown above. The angle that the rope makes with the vertical is closest to 0 2 kg E.45 F 10 N

Assume that the clay layer is preconsolidated, o128 kNm2, and Cs 15Cc. Estimate the consolidation settlement. Problem 1 Refer to the soil profile shown in Figure 1. Determine the total stress, pore water pressure, and effective stress at A, B, C, and D 3m 1.5 m 5 m Dry sand e 0.55 G, 2.66, Water table Sand G, 2.66 e0.48 Clay w 34.78 G, 2.74 D

For a normally consolidated clay layer, given Thickness 3.7 m Void ratio 0.82 Liquid limit 42 Average effective stress on the clay layer 110 kNm2 How much consolidation settlement would the clay undergo if the average effective stress on the clay layer is increased to 155 kNm2 as the result of the construction of a foundation

A sand has the following D10 0.2 mm, D60 0.4 mm, and void ratio e 0.6. a. Determine the hydraulic conductivity using. e 70.7825 k(cms) 2.4622 D07 (1 e) b. Determine the hydraulic conductivity using. 35 (1 0) C te k (cmsec) 35 10

A normally consolidated clay has the following values Vold ratio, e 1.2 1.9 k (cmsec) 0.2 x 10 0.91 x 10 Estimate the magnitude of k of the clay at a void ratio (e) of 0.9. Use Eq(1) x0

For a sandy soil, given void ratio, e 0.63 hydraulic conductivity, k 0.22 cmsec and specific gravity of soil solids, Gs 2.68. Estimate the hydraulic conductivity of the sand (cmsec) when the dry unit weight of compaction is 117 lbft. Use Eq. (2.37). Reference k x 1e

For a granular soil, given y 116.64 lbft, D, 82, w 8, and G, 2.65. For this soil, if emin 0.44, what would be emax What would be the dry unit weight in the loosest state

A saturated soil specimen has w 36 and yo 85.43 lbft. Determine a. Void ratio b. Porosity c. Specific gravity of soil solids d. Saturated unit weight (in lbft)

The moist unit weight of a soil is 119.5 lbft. For a moisture content of 12 and Gs 2.65, calculate a. Void ratio b. Porosity c. Degree of saturation d. Dry unit weight

A soil specimen has a volume of 0.05 m3 and a mass of 87.5 kg. Given w 15, Gs 2.68. Determine a. Void ratio b. Porosity c. Dry unit weight d. Moist unit weight e. Degree of saturation

A consolidateddrained triaxial test on a sand yields the results Allaround confining pressure 03 30 lbin Added axial stress at failure A0 96 lbin Determine the shear stress parameters (i.e.,p and c)

A clay soil specimen, 1.5 in. thick (drained on top only) was tested in the laboratory. For a given load increment, the time for 60 consolidation was 8 min 10 sec. How long will it take for 50 consolidation for a similar clay layer in the field that is 10ft thick and drained on both sides

For a normally consolidated soil, the following is given Pressure (kNm2) Void ratio 120 360 0.82 0.64 Determine the following a. The compression index, Cc b. The void ratio corresponding to pressure of 200 kNm2

Consider the circuit shown in Fig. 4.50. (a) If Is1 21s2 3 x 1016 A, determine Ve such that Ix 0.90 mA. (b) What value of Rc places the transistors at the edge of the active mode (a) VB (b) Rc V S2 H Rc Ix Q Q Figure 4.50 Vcc4.5V

A consolidatedundrained triaxial test was conducted on a saturated, normally consolidated clay. The test results are 03 13 lbin2 01(failure) 32 lbin Pore pressure at failure u 5.5 lbin Determine c, Q, c, and p.

Following are the results of two consolidateddrained triaxial tests on a clay Test I 03 140 kNm2 01 (failure) 368 kNm2 Test II 03 280 kNm2 01(failure) 701 kNm2 Determine the shear strength parameters that is, c and o .

A consolidateddrained triaxial test on a normally consolidated clay yielded a friction angle, , of 28. If the allaround confining pressure during the test was 140 kNm2, what was the major principal stress at failure

Unit Step Function Express each of the following functions in terms of the unit step function, then find its Laplace Transform. (a) (b) (c) (Trench 8.4.11) f(t) f(t) 0, sint, 0, t 0 f(t) te, 0

Consider the circuit shown in Fig. 4.81, where Is1 31s2 5 106 A, B 100, B 50, VA , and Rc 500 2. (a) We wish to forwardbias the collector base junction of Q by no more than 200 mV. What is the maximum allow able value of Vin (b) With the value found in (a), calculate the smallsignal parameters of Q and 22 and construct the equivalent

Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). Determine the coordinates of the center of the mass (or center of gravity) of the system.

A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water. The child then slowly walks to the other end of the canoe. How far does the canoe move in the water, assuming water friction is negligible?

a 60 kg man stands at one end of a 20.0 kg uniform 10.0 m long board. how far from the man is the center of mass

In the figure, a 60cm length of uniform wire, of 60 g mass and negligible thickness, is bent into a right triangle. The x and y coordinates of the center of mass, in cm, are closest to 10 cm 26 cm 24 cm

If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum 016 022 02 O 04 nints) rayity is g6. If a pendulum has a period Ton

Electric Field Magnitude A. A B. B C. C D. D E. E photobucket A.B.C.D.E An isolated sphere of radius R contains a uniform volume distribution of positive charge. Which of the curves on the graph above correctly illustrated the dependence of the magnitude of the electric field of the sphere as a function of the distance r from its center

Suppose that X decays by natural radioactivity in two stages to Y. The two stages would most likely be which of the following First Stage Second Stage Bemission with an antineutrino a emission A. B. emission C. B emission D. E. Emission of a deuteron a emission a emission with a neutrino y emission Emission of two neutrons y emission

Except for mass, the properties of the muon most closely resemble the properties of the A. electron B. graviton C. photon D. pion E. proton

A sample of N atoms of helium gas is confined in a 1.0 cubic meter volume. The probability that none of the helium atoms is in a 106 cubic meter volume of the container is A. 0 B. (106) N C. (1106)N D. 1 (106) N E. 1

For an ideal gas, the specific heat at constant pressure Cp is greater than the specific heat at constant volume C, because the A. Gas does work on its environment when its pressure remains constant while its temperature is increased. B. Heat input per degree increase in temperature is the same in processes for which either the pressure or the

Two coherent sources of visible monochromatic light form an interference pattern on a screen. If the relative phase of the source is varied from 0 to 27 at a frequency of 500 hertz, which of the following best describes the effect, if any, on the interference pattern A. It is unaffected because the frequency of the phase change is very small

A source of 1kilohertz sound is moving straight toward you at a speed 0.9 times the speed of sound. The frequency you receive is A. 0.1 kHz B. 0.5 kHz C. 1.1 kHz D. 1.9 kHz E. 10 kHz

Two wedges, each of mass m, are placed next to each other on a flat floor. A cube of mass M is balanced on the wedges as shown above. Assume no friction between the cube and the wedges, but a coefficient of static friction 1 between the wedges and the floor. What is the largest M that can be balanced as shown without motion of the wedges D. m m

The magnitude of the Earths gravitational force on a point mass is F(r), where r is the distance from the Earths center to the point mass. Assume the Earth is a homogeneous sphere of radius R. Suppose there is a very small shaft in the Earth such that the point mass can F(R), be placed at a radius of R2. What is F() A. 8 B. 4 C. 2 D. 12 E. 14

A football of radius R is kept on a hole of radius r (r R) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle 0 from the horizontal as shown in the figure below. The maximum value of 0 so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale) S N (A) rotate in

A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves witho slipping on the axle, and the

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale) Light (A) (C) Air Glass B (B) (D) Air

An openended Utube of uniform crosssectional area contains water (density 10 kg m). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a waterimmiscible liquid) of density 800 kg m is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio of the heights of the liquid in

The filament of a light bulb has surface area 64 mm. The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take StefanBoltzmann

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows position X Speed X acceleration XP Linear momentum X force X. Then (A) ap2B (C) pqra (B) pqrB (D) pqrB

A uniform electric field, E 4003 NC is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 210x10 ms. This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure. Take 10 Ckg. Then m,5m (D) time

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity p. Its inner radius is R and outer radius is R. If a voltage Vo is applied between its two ends, a current I flows in it. In addition, it is observed that a transverse voltage AV develops between its inner and outer surfaces due to purely kinetic effects of

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO4) of different concentrations n, and n (nn) molecules per unit volume with An (nn)

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at

One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0,0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole p pointing towards the charge q is fixed at the origin, the spring gets

Consider one mole of helium gas enclosed in a container at initial pressure P, and volume V,. It expands isothermally to volume 4V. After this, the gas expands adiabatically and its volume becomes 32 V. The work done by the gas during isothermal and adiabatic expansion processes are Wiso and Wadias respectively. W. iso If the ratio f In2, then fis

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms, the smallest value of the

A circular disc of radius R carries surface charge density. (r) 0.17). , where is a constant and r R is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the R charged disc completely is . Electric flux through another spherical surface of radius and concentric 4 with the disc is . Then the

The diagram shows changing wavelengths along the electromagnetic spectrum. Which labels belong in the areas marked Y and Z? Y: Ultraviolet Z: Radio Y: Gamma rays Z: Visible light Y: X-rays Z: Infrared Y: Radio Z: Gamma rays.

The diagram shows changing wavelengths along the electromagnetic spectrum. which labels belong in the areas marked X and Y. Ultraviolet Z Raadio Y Gamma ray Ultra violet Infrared JL. Xrays Visible Microwave 104 10 1 107 105 10 www.z Wavelength (nm) 10 104 106 Radio 10 N 10 Energy (eV) 10 101 103 105 107

A mass of 75 kg is suspended from a spring of stiffness 15kNm of extension. When the mass is slightly displaced from equilibrium, it vibrates freely with an amplitude of 36mm. Determine (i) The periodic time of the system 1 mark,(ii) The frequency of vibration,(iii) The velocity and acceleration when the mass is displaced 16 mm from the

Obtain the equation of motion and its solution for the vibration of a body of mass m when acted upon by a restoring force of N per unit displacement from the position of static equilibrium, and subjected to a damping force c N per unit velocity. 6 marks

Obtain an expression for the natural frequency of torsional vibration of an elastic shaft carrying two rotors, one at each end. 4 marks

For the circuit shown in Fig.1 (i), find (i) the output voltage (ii) the voltage drop across series resistance (iii) the current through zener diode. R5k I IL Iz LE 120 V 50 V www. 10

For the circuit shown in Fig. 2 (i),find the maximum and minimum values of zener diode current. 5 www. 80120 V I Iz IL 50 V 10 Fig.2 5 I 80120 V (ii) Iz IL 50 V 10

A 7.2 V zener is used in the circuit shown in Fig. 3 and the load current is to vary from 12 to 100 mA. Find the value of series resistance R to maintain a voltage of 7.2 V across the load. The input voltage is constant at 12V and the minimum zener current is 10 mA. E 12 V. I R Fig. 3 Iz Vz IL RL Eo

The circuit of Fig. 6 uses two zener diodes, each rated at 15 V, 200 mA. If the circuit is connected to a 45volt unregulated supply, determine (i) The regulated output voltage (ii) The value of series resistance R. E 45 V R Fig. 6 Z Z R Eo

What value of series resistance is required when three 10watt, 10volt, 1000 mA zener diodes are connected in series to obtain a 30volt regulated output from a 45 volt d.c. power source

How many board feet are contained in a 2x4 stud 8 long If the stud costs 2.36, what is the cost per board foot Show calculations.

a) 2 mA b) 4 mA c) 6 mA d) 8 mA e) 10 mA

Based on the information from the picture, the collector current Ic is equal to

a) Ic= 1.1 mA, Vce =4.96V b) Ic= 2.17 mA, Vce =10 V c) Ic= 41 mA, Vce =5V

The Q point of the circuit attached is best defined by

Based on what is given in the picture, the voltage at the base VB is O2.12V 3.12V 4.12V 5.12V

Given that Ic is 2mA and VCE 10V, determine the value of R1 in the circuit that follows

A pickup truck with mass 1.80 x 10 kg is traveling eastbound at 15.0 ms, while a compact car with mass 9.00 x 10 kg is traveling westbound at 15.0 ms. (See figure.) The vehicles collide headon, becoming entangled. (a) Find the speed of the entangled vehicles after the collision. (b) Find the change in the velocity of each vehicle. (c) Find the

In the same circuit before, under the same conditions, determine the value of Rc Ic2mA and Vce10V

Calculate the lattice constant of NaCl Crystal. The density of NaCl is 2189 kgm and Avogadro number (N) is 6.02x1026 kgmol.

For a simple cubic crystal find (i) the ratio of intercepts on the three axes by (1.2 3) plane, (ii) the ratio of the spacings of (110) and (111) plane and (iii) the ratio of nearest neighbour distance to the next nearest neighbour distance.

Sodium transform from bodycentered cubic to hexagonal closepacked crystal structure at 23 K without change of density in the cubic face a4.23 A and in hexagonal closepacked face1.63. Find lattice constant in hexagonal closepacked face. a

Find the Miller indices for planes in each of the following sets which intercepts a, 5 and at (i) 3a, 3b, 2c (ii) a, 2b, o (iii) a, b2, c (iv) 3a, 2b, 2c

Silicon has diamond structure with untilcelledge a0.542 nm. The interatomic separation is (a) 0.122 nm (d) 0.542 nm GATE 2002 (b) 0.234 nm (c) 0.383 nm

A simple cubic crystal with lattice parameter a under goes transition into a tetragonal structure with lattice parameters a, b 2a and c, 2 a, below a certain temperature. The ratio of the interplanar spacings of (101) planes for the cubic and the tetragonal structures is GATE 2012 1 CAREEN SHE CAVOUR (a) (b) 6 (c) 8. (d) 8

F Prove that momentum operator 2x US harmitian.

Prove That Hamiltonian operator is harmitian.

Prove that harmitian operator have real eigen values.

Two eigen functions of harmitian operator belonging to different eigen values are on thogonal Prove. V.U 2009 21

If two harmition operators commute then their product is also harmitian operator Prove 11

A body floats in a liquid with one fourth volume out of liquid. The same body floats in water with its one third volume out of water. Find density of liquid.

In figure a capacitor of capacitance 2uF is connected to a cell of emf 20 V. The plates of the capacitor are drawn apart slowly to double the distance between them. Calculate work done by the external agent on the plates. 207

The airplane is traveling in a straight line with a speed of 300 kmh, when the engines A and B produce a thrust of TA 40 kN and TB 20 kN, respectively. Determine the angular velocity of the airplane in t 5 s. The plane has a mass of 200 Mg, its center of mass is located at G, and its radius of gyration about G is kg 15 m. TA 40 kN 8 m A B TB

Three point charges Q 1 , Q 2 , Q 3 are places along a straight line with equal space.Q 2 and Q 3 are equal in magnitude but opposite in sign.If net force on Q 3 is zero.The value of Q 1 is?

As a model of a linear triatomic molecule (such as CO). consider the system shown in Figure 11.21, with two identical atoms each of mass m connected by two identical springs to a single alom of mass M. To simplify matters, assume that the system is confined to move in one dimension. (a) Write down the Lagrangian and find the normal frequencies of

Two spheres A and B of radius 4 and 6cms are given charges of 80 and 40 micro coulombs respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is?

There are three identical capacitors, each of capacitance Care connected as shown. The emf of the cell connected is Find the charge flows through the switch when it is closed. E

Fig. 11 shows regulated power supply using a zener diode. What will be the circuit behavior if (i) filter capacitor shorts (ii) filter capacitor opens F Fuse blows as a result of excessive current o eeeeeee eeeeeee D D3 DA C shorted Fig. 11 Electron flow R RL

Fig. 10 shows the basic zener diode circuits. What will be the circuit behavior if the zener is (i) working properly (ii) shorted (iii) opencircuited 12V Vz 6V 1kQ (i) www V 6V 5 12V 1kQ2 Zener short (ii) Vo OV 5kQ2 Fig. 10 12V 1kQ2 Zener open (iii) V 10V 5kQ

In the circuit shown in Fig.9,the voltage across the load is to be maintained at 12 V as load current varies from 0 to 200 mA. Design the regulator. Also find the maximum wattage rating of zener diode. 16 V R www Iz Fig. 9 IL RL Eo

Over what range of input voltage will the zener circuit shown in Fig. 8 maintain 30 V across 2000 2 load, assuming that series resistance R 200 2 and zener current rating is 25 mA R 200 S2 Fig. 8 Iz IL 2000 www Eo

The electric field and magnetic field in free space are given by E H 50 cos(10 t Bz) a Vm Ho cos(10t z) ap Am Express these in phasor form and determine the constant H, and such that the fields satisfy Maxwells equations. The instantaneous form of E and H are written as E Re(Esejat), H Re(Hsejwt), 106 The phasor Es and Hs 50 So ejzag P

determine the phasor form of and the instantaneous form of

The electric field and the magnetic field in free space are given by 50 R cos(106tBz) Vm cos(106tBz) Am Ho R Express these in phasor form and determine the constants H, and such that the fields satisfy Maxwells equations.

Using Maxwells Equations. The electric field intensity for a wave propagating away from a pointlike source is given in phasor form as jR o a) Use the differential form of Faradays induction Law to determine the corresponding magnetic field intensity associated with this electric field. b) Show that the time average power density (the time average

Maxwells equations for the electric field E(r) and the magnetic field B(r) in a charge and currentfree region are (i) (ii) V.E0 OB t 1 8 c t 7) E 1 V.B0 VXE By considering V (V E), use Maxwells equations and an appropriate vector identity to show that E 0 Hence obtain an expression for the constant c. Find a similar equation for the magnetic

A metal bar 70 cm long and 4.00 kg in mass is supported on two knifeedges placed 10 cm from each end. A 6.00 kg load is suspended at 30 cm from one end. Find the reactions at the knife edges. (Assume the bar to be of uniform cross section and homogeneous.) (a) R 64.88 N R 33.12 N (c) R 43.12 N R 43.12 N (b) R 54.88 N R 43.12 N (d) R, 33.12

Two identical loudspeakers are fed the same signal which generates sound of wavelength 8. The speakers are facing each A other, separated by a distance 48. At what minimum distance in front of a speaker, and on the line connecting them, is the local sound intensity a minimum A) (714) 8 B) (4) 8 C)(4)8 D) (4) 8 5. Two identical loudspeakers (S1 and

Two loudspeakers are placed d 3 m apart and facing the same direction. The loudspeaker diaphragms are vibrating in phase with each other, producing a single frequency sound with a wavelength of A1.2 m. (a) Determine approximately the distance between the points on the wall on the right where the sound will be the loudest. loudspeakers X 4.5 m (b)