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Physics Questions and Answers October 16, 2022

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For the circuit shown below, assume that the OpAmp is ideal. which one of the following is true,Vo R ww ww 2R ww 2R R R Which one of the following is TRUE O V V OV 1.5 V OV2.5 V OV5V 0 R win V

For the circuit shown below, talking the OpAmp as ideal, the output voltage Vout in terms of the input voltages V, V2 and V3 is,V V o V0 192 ww www 1 ww 4 V. V 4 01.8V7.2VV 02V8V9V3 O 7.2V 1.8VV O8V2V9V3 3 992 ww Vcc V SS out

O O V 10 V. 5 10 V,The transfer characteristic for the precision rectifier circuit shown below is (assume ideal OpAmp and practical diodes) 20V 4R Vwww R D R www D V.

In the figure, D is a real silicon pn juction diode with a drop of 0.7 V under forward bias condition and D is a Zener diode with breakdown voltage of 6.8 V. The input Vm(t) is a periodic square wave of period T,,Whose one period is shown in the figure. 147 14V 7.5 V and 20.5 V 6.1 V and 21.9 V 7.5 V and 21.2 V O 6.1 V and 22.6 V 10F HH t (sec)

Consider the following circuit using an ideal OPAmp. The IV characteristics of the diode is described by the relation. 1 ( 1 1) forward bias) 0.1 V where V 25mV, I, 1uA and V is the voltage across the diode (taken as positive for O 0.7V O 1.1V VIVO ww 100 For an input oltage V1, output voltage V, is OV 4k0 www KH

The switch K is closed at t0. Find i(0) i (0)2A (0) 1A voor 2H O ov O 0.1 V O 0.7V 1.1V 2H i(t) t0

A 4 bit ripple counter and a 4 bit synchronous counter are made using flipflops having a propagation delay of 10 ns each. If the worst case delay in the ripple counter and the synchronous counter be R and S respectively, then R 10 ns, S 40 ns R 40 ns, S 10 ns R 10 ns, S 30 ns R 30 ns, S 10 ns

The simplified logic expression for the below circuit A. RS UV T S. (RUT) (SV T) O (RS) T (U V) T RSUV RS UV RTV UTS B 4

The circuit shown below is used to implement the function, z f(A,B) A B, the value of P and Q are PA A OPA, QB OPB, QA OPB.Q0 OP0,QB Z

When the Boolean function, F(x,x,3)(0,1,2,3)d (4,5,6,7) is minimized, what does one get,01 0 0 OX 0 N3

In the amplifier circuit shown in the figure, the values of R, and R, are such that the transistor is operating at V 3V and I1.5 mA when its 3 is 150. For a transistor with 3 of 200, the operating point (VCE Iis R www O (2V, 2mA) O (3V, 2mA) O (4V, 2mA) (4V, 1mA) Vcc6V R T

In the circuit shown below what is the output voltage (Vout) if a silicon transistor Q and an ideal opamp are used 5V 15V O0.7V O 0.7V 15V 1kQ 15V 15V Q V OUT 4

In the circuit shown below, the average power dissipated by the transistor is in mW 50 O 3.87 4.5 9.5 10 9V 0.5 mA 4.7kQ 9V B49 VEB 0.7V

BE The circuit using BJT with B50 and VB0.7 V is shown in the figure. The base current I and collector voltage Vare respecively,430 H 10F 43 mA and 11.4 V 40 mA and 16 V 45 mA and 11V 50 mA and 10 V wwww 1 www 40F 2017 OVC

O ABBCCA AB AC BC OCAB AB OC(AB) AB,Consider the following truth table ABC F 00 0 1 00 010 0100 0 1 1 0 1001 10 1 0 1 1 110 1 1 1 1 0 The logic expression for F is

The frequency of the pulse at z in the network shown in figure below is W 4Bit Parallel Counter 4Bit Johnson z Counter 10Bit 160 kHz Ring Counter 10 Hz 160 Hz 40 Hz 5 Hz Mod25 Ripple Counter

A sequential circuit using Dflipflop and logic gates is shown below where X and Y are the inputs and Z is the output. The circuit is CLK SR FF with inputs X R and Y S SR FF with inputs X S and Y R OJK FF with inputs X J and Y K O JK FF with inputs X K and YJ D N Z

Which of the following is the output Yo,1 0 A AB 01 Do A D Ao D D3 2bit Encoder D 1x4 Io DE I 1 Do MUX 1 13 S So D B 2bit Decoder D D D Do

Consider the combinational logic circuit shown below 0 1 2 3 1 1 1 S S (0) A B The output Q can be expressed as m(0,1,2,3,4,5,6), (0,1) m(1,2,3,4,5,6)

The MODnumber of asynchronous counter, considering J and K input 1. Shown in the figure below is. CLK K Q CLK K CLK K CLK K Q CLK K Q. (MSB) CLK,20 24 26 18

For the BJT circuit shown, assume that the 3 of the transistor is very large and V0.7V. The mode of operation of the BJT is 2V cutoff saturation normal active reverse active 10 10V

The collector voltage V of the circuit shown in the given figure is approximately 3 is very large. 201 20kQ 2V 4.6V 8V 8.6V 10V 2kQ Vc 4.3kQ

In 2021 your firm had 5 computers each with a market value of 4,000. In the same year you spent 1,000 for their maintenance and upgrading, and purchased 2 new computers each with a market value of 2,000. By the end of 2021, the total market value of your original 5 computers had dropped to 3,000 (others remained the same). Now we are in 2022.

Consider a hydrogen atom undergoing a 2p1s transition. The frequency (v) corresponding to this transi tion is 2.47 x 105 Hz and the lifetime of 2p state for spontaneous emission is 1.6 ns. Assuming that the refractive index (no) of the medium is 1, the coefficient of stimulated emission B, (v) for this transition is given by 0.109 x 10 m W sec

A diatomic molecule has vibrational states with energies E, co (v 1). where vand Jare nonnegative integers. In the rotationalvibrational spectra of diatmic molecule, spectral lines in Pbranch and Rbranch are observed. Match the lines given in ColumnI with their energy given in ColumnII. ColumnI A. R line B. R line C. Pline D. P line A3, B1, C4,

If the coefficient of stimulated emission for a particular transition is 4.2 x 101 m W s and the emitted photon is at wavelength 6000 A, then the lifetime of the excited state is approximately. 80 ns 310 ns 230 ns 155 ns 4

The ground state of chlorine is 2P32. The magnetic dipole moment corresponding to total angular momentum is (where g is Bohr magneton) 15 HB 254B HB 15 HB 4

10.6 cm1 and 6.5 cm1,The rotational constant (B) for H 35Cl is observed to be 10.6 cm. The values of rotational constant (B) for H 37Cl and 2D 35CI, respectively are 5.5 cm1 and 10.6 cm1 10.6 cm and 5.5 cm1 5.5 cm1 and 11.6 cm1

The spectroscopic symbol for the excited state of sodium is P32. Under the action of a strong magnetic field (when LS coupling can be neglected) the excited state energy level will split into 3 levels 4 levels 6 levels 5 levels

The fundamental and the first overtone frequency of the diatomic molecule HCI behaving as an anharmonic oscillator are found to be at 2886 cm and 5668 cm1 respectively. If the reduced mass of HCI is, then the force constant of the molecule is 479 Nm 517 Nm1 573 Nm 592 Nm 4

The first excited state of the rotational spectrum of the nucleus 233 U 92 has an energy E keV above the ground state. The energy of the third excited state (in keV) is 10 OE 3 2 2 E 4

Two protons each of energy 500 MeV approach each other from opposite direction. If the only interaction is the electrostatic interaction, then the closest distance the protons comes to each other is O 1.21 x 1015 m O 1.44 x 1015 m O 1.44 x 1016 cm O 1.21 x 1016 cm

The cross section of the machine part is a square, 5 mm on a side. If the maximum stress at section mn is limited to 150 MPa, determine the largest allowable value of the eccentricity e. 250 N m FIG. P8.14 250 N P FIG. P8.15

Two fermi gases made of particles with spins 52 and 12 have their fermi energies in the ratio 1 3. The ratio of particle densities of these gases in two identical gas cylinders will be 4,012 13 61 O31

The number of microstates for a microcanonical ensemble is given by QaE52, where a is a constant. The equation of state and the adiabatic exponent for the system is 4 3 O PV kgT PV akgT 3 2PV akgT 2PV akgT 6 5 5 3

A system in thermodynamic equilibrium has four single particle energy levels 0, , 2 , 3 with degeneracies 2, 2, 1, 2 respectively. The probabilities of existence of each molecule in these energy levels are 0.25, 0.25, 0.30, 0.20 respectively. What is the entropy of each molecule 4,Ok 0.5 In 80.3 In 30.11n10 Oks In 220.5In100.3 In 3 Ok, In 220.5 In

38 18 12,A partition divides a container of volume V in the ratio 2 1. The container is filled with ideal gas with ratio of pressures and temperatures on both sides equal to 13 and 1 2 respectively. On removing the partition, the equilibrium temperature becomes 1021

The molar internal energy of one mole of a Vander waals gas is U cT aV, here V is the molar volume, a is one of the constants in the equation of state and c is a constant. What is the value of molar heat capacity Cp C 1 C R 2a(Vb) RTV3 1 R 2ab aV PV RV3 PVaV 2ab 4

An optical cavity of volume 2 cm has central frequency v 1018 and can support 103 modes of vibration, the wavelength range admissible for the cavity is 3100 m to (3(1.610))10 O 3100 m to (3(1.610))10 m 3x102 m to (3(1.61010))x102 m 310 m to (3(1.610))10 m

A system of N distinguishable quantum harmonic oscillators is at thermal equilibrium temperature T. The mean square value of the momentum of the system is ,Where Nm Nhom sinh O Nho 2m Nhom 2 coth coth 1 KBT Bo 2 Bo 2 Bho 2

An ideal gas with volume V and pressure P is made to expand adibatically to volume V and pressure P2. This is followed by isobaric compression to (P2, V1), followed by increase in pressure to P, keeping volume constant at V. What is the efficiency of the cycle (Here, gamma is adiabatic constant of gas) 1 P 1y 17 1 V V V V R P P R 1

A system in thermal equilibrium with a heat reservoir at temperature 105 K has particles that occupy single particle levels and obey Maxwell Boltzmann statistics. What will be the energy of the level that has half the population of the energy level with energy 20 eV Use kg 8.6x105 eV 26 eV 15 eV,30 eV 5.96 eV

The mean square fluctuation in energy of a system in thermal equilibrium at temperature T is proportional to (where Cy is the heat capacity) OTCy T O TC OTCT OTIC

Consider a system of three classical and noninteracting particles in contact with a thermal reservoir at temperature T. Each particle may occupy any of the three nondegenerate energies, 0, and 3 The average energy per particle in high temperature limit is 02 3 04 3 04 02

A system of 5 localized and independent quantum oscillators is in contact with a thermal reservoir at temperature T. The energy levels of a single oscillator are given by,E oxn1), The average internal energy of the system is o 01 o 2 5 w 2 131000 2 O 15 2 ekr 1 5w 700 ek 1 200 200 e w RT 1 10w 2000 e RT 1 n 1,3,5,7......

a 4Rb a 4Rb a 4Rb,One mole of a hypothetical gas follows the equation of state P(V b) RT exp (aRTV) where both a and b are constants and other symbols have their standard meanings. The critical temperature of the gas is a 4Rb

A classical monoatomic ideal gas is subjected to potential that corresponds to a force proportional to the fourth power of position (r). The specific heat per particle of the gas is 0.6 KB 2.1 KB 1.5 KB 2 KB

The first excited state of 182W is 2 and is 100 keV above the ground state. The energy of third excited state of 182W is 583 keV 333 keV 100 keV 700 keV

2 cosh Bo kBT 3 2mk T v (2 mkg)( h 2 ( 2V cosh ) 3 20 (1) (2 x mk z T) 2V cosh h 2mkgT uBo KBT 3 ) coch() cosh 7N,A cubic box with infinitely hard walls having volume V. contains a nonrelativistic classical ideal gas consisting of Nmolecules, each of which has mass m. spin and magnitude of magnetic moment u. The partition function of the gas in

The transition temperature of YBCO superconductor is about 92K. The superconducting energy gap (Eg) according to BCS theory is 9 meV 28 meV 36 meV 7 meV

Sodium metal with a bcc structure has two atoms per unit cell. The radius of the sodium atoms is 1.85A. If the classical value of the mean free time at 0C is 3x1014 s, The value of its electrical resistivity at this temperature is ,4.46 10m 02.23x10 m 08.92 x 10m 06.23x10 m

The powder diffraction patterns of a fcc crystal recorded by using Cuk, radiation of Xray. If the rays diffracted in such way that for second smallest peak the braggs angle is 60, then the lattice parameter is 3.08 5.34 5.43 3.80A

Cd atom show hcp structure with lattice parameter a 297.94 pm and c 561.86 pm. The density of the crystal is approximately. 87.136 kgm3 8713.6 kgm 5809.06 kgm 58.09 kgm

An Xray beam having energy of 5 keV used to determine crystal structure of a solid with lattice parameter a 1.24 A. The Braggs angle for (001) plane is 30 45 60 90

The heaviest pebble of mass m that can be moved by a stream is known to be proportional to some powers of the speed of the stream v. the density (of water) p and the acceleration due to gravityg. Using dimensional analysis, we may conclude that m is proportional to pv4 g 6.0 g 6.0 g

Three bodies A(mass m), B(mass 2m) and C (mass m) are kept on xaxis in order ABC, as shown in figure. Now, the body A is given a velocity v along the xdirection. All the collision are elastic. Body C rests on a rough surface with coefficient of friction u. The time taken by body C to stop, is A T (Here, g is acceleration due to gravity) 8v 3ug

An ideal Bose gas undergoes BoseEinstein condensation with Bose temperature TB. The variation of number of particles in the ground state (Ng) and in the excited state (Ne) with temperature is shown below N., N. N DXC N Tc The value of Tc (as shown in the graph) is N N N 232 T

Consider a system of N distinguishable particles (in which particles can move in one dimensional segment q 0 and q L) in thermal equilibrium at temperature T. The single particle Hamiltonian is given by (1) The partition function of the system is given by H 2m a en 2mkT (2) ate (2) aln h 2mkT h where a is positive constant and L, is

An absorption line found at 5A for stationary galaxy is shifted to 4A for a galaxy A. The speed with which galaxy A is moving with respect to the stationary galaxy is, 9c 41 9c 41 away from it O 16c 41 towards it O 16c 41 towards it away from it

The length of a rod of proper length 10 m is 8m as seen from a frame S that is moving parallel to its length. A particle at rest in the frame of rod decays in 20 ns. The lifetime of the particle as seen from frame S is 25 ns 16 ns 30 ns 22 ns

A rocket moving directly away from earth with speed emits a spaceship with speed along its direction of motion. If r 20 sec elapses in a clock at rest on earth as seen by an observer on earth, then the time elapsed as seen by the spaceship is 130 30 S 260 30 S O 130 50 260 50 S S

The gas phase reaction A2B 2C, which is first order in A and first order in B is to be carried out isothermally in a plugflow reactor. The entering volumetric flow rate is 2.5 dm3min and the feed is equimolar in A and B (and no C). The inlet temperature and pressure are 727C and 10 atm, respectively. The specific reaction rate constant at this

A particle of mass m is moving in a potential V(x) cx where c and d are constants. The period of small oscillations about equilibrium point is x 27. 2 m 4c 2, m 4c 2m C m 8c 4

A reference frame is moving at 0.8c in the zdirection with respect to a frame S. An event occurs in S frame with coordinates (x, y, z, ct) (1, 0, 2, 3). The coordinates (x,y,z,ct) of the event with respect to S frame is (1,0, 1,6) 19 (1,0,23213) 22 (27,0,1,19) 3 O (0,1,7,6)

A proton and an antiproton having rest mass 1 GeVc travelling with the same speed collide with one another from the opposite direction. If the rest mass of the particle created is 4Ge vc, then the speed with which the original particles were travelling is, 2 O 3c 3 O 3c

Consider a sphere of radius R, the magnetic vector potential inside and outside the sphere are given by A(r,0,0) kR cos Ho 3 1 KR 3 r The surface current density on the sphere is O kR sin Mo O kRcos O kRsin 0 Mo k Rr sin 80 r R 06

A charge q files with speed v0.8c parallel to xaxis at height z h above the xy plane. The magnetic field at the origin w.r.t. lab frame hen it cross the zaxis is 5q () 16 ch 3q () 16ht Hogc 3h Hoqc 4 h

The current flowing through a long solenoid of radius a is varied in such a manner that the axial magnetic field inside increase with time according to the law, B 2Bot, where B, is a constant. The magnitude of the displacement current density inside the solenoid is 0 Botr Ho O Bor Bor Mo

Decrease by a factor 0.25 Increase by a factor 0.25,A charge particle rotating in a circular path of radius R with speed v keeping speed constant if we increase the radius 2R. The power of the electromagnetic radiation will Decrease by a factor 0.5 Increase by a factor 0.5

Consider a statistical system composed of two photons moving in a segment of length L. The volume of the phase space enclosed by the surface at constant energy E is (where c is the speed of the light). 02E1 O EL EL 2c O 4EL c

One gram of water at 300K is poured down gently into a lake of 400K. The change in the entropy of the universe when the temperature of the water has reached 400K is (in units of calK) 4 In 3 In In In 43 4 1 4 2 1 3 4 3) 4 4

A particle of mass M moves along the xaxis under the influence of the potential energy V(x) kx exp(ax). where k and a are positive constants. The period of small oscillations about the equilibrium position is 4,TeM 2 2ak eM ak 2 2. eM ak eM 2ak

A body of mass mis projected with speed u in a medium that exerts a resistance force of magnitude F mkv. where k are positive constants and is the velocity of the body. Gravity can be ignored. Assuming that the motion starts from the origin and takes place along the positivexaxis, then which among the following state ments is incorrect The

A O 2 ms Olms O 3 ms O 0.5 ms O 3 B,A hollow cylindrical pipe of length 4 m rotates with constant angular speed 1 rads about a vertical axis through the centre O. A particle is initially at rest in the pipe at a distance 3 m from O. Assuming no frictional forces, the speed of the particle as it leaves the pipe is

A player kicks a football from ground level at 27.0 ms at an angle of 30.0 degrees above the horizontal. Find a) its hang time (time that the ball is in the air),b) the distance the ball travels before it hits the ground, and c) its maximum height.

The equation of state of a system is pbTV, where b is a constant. The entropy S of the system is a function P of temperature only. i.e., S f(T) and the internal energy is U mT In V, where n and m are some constants. The constants b. m. n are related as Om2n, b3 Om2b, n 3 Om 3n, b 2 Om 3b, n 3 4

100 g of a liquid at 30 C and with specific heat capacity 30 cal g K is heated in a pan. If its temperature is raised to 333 C, then the factor by which the number of microstates change is exp(6.2 103) exp(6.2x105) exp(6.2106) O exp(6.2x1024)

A pion at rest decays into a muon and neutrino (). Rest masses of particles are m. m, and m 0. If t is the proper life time of u and c is velocity of light, on the average the distance travelled by muon in vacuum before disintegrating is m m mmu m (mm 2mm m CT 2m mu m ) et (m m) c 2mm CT

Al decays to excited state of Si emitting Beta particles with maximum kinetic energy equal to 2.865 MeV. Si in the excited state decays to the ground state via y emission. The energy of the photon emitted is Given Mass of Al27.981908 amu and mass of Si27.976929 amu 1.77 MeV 2.24 MeV 4.58 MeV 6.32 MeV

A plastic block of 0.8m width, 0.6m height, and 1.2m length is floating in a swimming pool. Find the height of the plastic block above the water surface and the specific gravity of the plastic is 0.95.

What would be the specific weight, density, and specific gravity of a material with a mass of 12 pounds and volume of 3 cubic inches?

The dispersion relation of a gas of spin fermions in two dimensions is E hulk, where E is the energy, k is the wave vector and v is a constant with the dimension of velocity. If the Fermi energy at zero temperature is er, the number of particles per unit area is 1. (F(4mvh) 2.me(3vh) 2. e(6nvh) 4. (2nv)

A particle of mass mis confined in infinite potential well. V(x) Initial state of the particle is . Asin 0 0

According to shell model, the nuclear magnetic dipole moment of the Bi(209,83) nucleus is Given that for a proton g, 1. g. 5.5857, and for a neutron g, 0. g, 3.826

An aluminium target is bombarded by a particles of energy 7.68 MeV and the resultant protons were detected at 90 with energy 8.36 MeV. The reaction is given by He(4,2)Al(27,13) P(1,1)Si(30,14)Q. The Q value of the reaction is

Roman and Tej decide to have a friendly race with their race cars on a straight road Romans car can accelerate at 20 meters per second per second and can achieve a maximum speed of 60 meters per second. This means once he reaches 60 ms, his car will maintain a constant speed. Tejs car can only accelerate at 15 ms2, but can handle a speed up to 75
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C. A person is leaning against a wall with her hand straight out pushing against the wall. Compare the force exerted by her hand on the wall to that exerted by the wall on her hand. What is the type of force exerted by the wall on her hand called d. In (c), is the force exerted by the wall on the persons hand passive or ac tive Explain. e. In (c)
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An electric motor has an efficiency of 75% when running at 1450 rev/min. Determine the out-put torque when the power input is 3.0 kW.

The graph at the right shows the atomic radius for the 19 elements in the periodic table. (a) Describe the trend in atomic radius in going from H (atomic number 1) to K (atomic number 19). (b) Find the three elements represented with blue dots on a periodic table. What do their placements in the table have in common (c) Find the three elements

A point mass m, is constrained to move on the inner surface of a paraboloid of revolution x2 y2 az (where a0 is a constant). When it spirals down the surface, under the influence of gravity (alongz direction), the angular speed about the zaxis is proportional to (a) 1 (independent of z) (b) z (c) z (d) z

Two coupled oscillators in a potential V (x, y)12 kx2 2xy 12 ky2 (k2) can be decoupled into two independent harmonic oscillators (coordinates x,y) by means of an appropriate transformation 0 (a) (b) . The transformation matrix S is 25 2 (c) (d)

A heavy particle of rest mass M while moving along the positive z direction, decays into two identical light particles with rest mass m (where M2m). The maximum value of the momentum that any one of the lighter particles can have in a direction perpendicular to the z direction, is (a) CM 4m (c) CM4m (b) CM2m (d) MC 2

A function of a complex variable z is defined by the integral f(z)fai.r (w222z), where I is a W2 WZ circular contour of radius 3, centred at origin, running counterclockwise in the w plane. The value of the function at z(2i) is (a) 0 (b) 14i (c) 8x2i (d) 2 i I 27

An idealised atom has a nondegenerate ground state at zero energy and a gfold degenerate excited state of energy E. In a noninteracting system of N such atoms, the population of the E excited state may exceed that of the ground state above a temperature T The 2k, In 2 minimum value of g for which this is possible is (a) 8 (b) 4 (c) 2 (d) 1

Let InI denote the energy eigenstates of a particle in a onedimensional simple harmonic potential V(x)mox. If the particle is initially prepared in the state y (1 0)) (10) 1)), the minimum time after which the oscillator will be found in the same state is (a) 3(20) (b) w (c) (20) (d) 2w

The wavelength of the first Balmer line of hydrogen is 656 nm. The wavelength of the corresponding line for a hydrogenic atom with Z6 and nuclear mass of 19.9210 kg is (a) 18.2mm (d) 393.6mm (b) 109.3nm (c) 143.5mm

The velocity v(x) of a particle moving in one dimension is given by v(x)v, sin where Xo V, and x, are positive constants of appropriate dimensions. If the particle is initially at xx , where e 1, then, in the long time, it (a) Executes an oscillatory motion around x 0 (b) Tends towards x 0 (c) Tends towards x x (d) Executes an oscillatory

An aircraft has the following short period approximation Find the natural frequency, damping ratio, and the steadystate value of AOA in response to a unit step input using the final value theorem.

Ion Implantation A silicon substrate is doped ptype at 1105 cm. Arsenic is implanted into the wafer at an energy of 85 KeV, after which Si is epitaxially grown to bury the implanted profile. This results in a projected range of 0.5 m and a normal straggle of 18 nm. Assume a Gaussian profile. a. Calculate the dose required for a peak Arsenic

An intrinsic germanium crystal has a hole density of 109 m3 at room temperature. When doped with antimony, the hole density decreases to 1017 m3 at the same temperature. Calculate the majority carrier density. (101 m)