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Physics Questions and Answers October 30, 2022

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The function (AB) is to be realized using only 2input NAND gates. The minimum number of 2input NAND gates required for such a realization is

Suppose J, (x) and J, (x) are two linearly independent solutions of the differential equation xy xy (x v) y 0 (v is half integer) Then, the value of J2 (x)J2(x) is equal to 12 x. (An integer)

The spin state of an electron in Sbasis is given by 1 1 x) 5 2i The uncertainty in the measurement of S, for the particle is . (Upto one decimal place)

The total power emitted by a spherical black body of radius 1 unit at a temperature T is 1 unit. The total power emitted by another spherical black body of radius 0.25 unit at a temperature 3T, will be units. (Upto two decimal places)

The number of spectroscopic terms resulting from the LS coupling of a 2s2p electron is .(Answer should be an integer)

In copper at 1000 K, the energy at which the probability that a conduction electron state will be occupied 0.90 is eV. (Given the fermi energy of the copper is 7 eV). (Round off to two decimal places)

For a system, Lagrangian is L9 bracket (p. H) is q1 2 29 If H is the corresponding Hamiltonian then the value of Poisson The value of a is (Answer should be an integer)

The following signal V of peak voltage 8V is applied to the noninverting terminal of an ideal opamp. The transistor has VBE 0.7 V. B100 VLED 1.5 V, Vcc10V and Vcc 10V. 10V 10V 8kQ 2kQ Vcc 15k w Vcc The number of times the LED glows is 100 LED Vin 6 V 4 V 2 V 0 2 V T U

A particle of mass m is moving under an attractive delta potential V(x) V8 (x) V 0 and the particle is initially in the ground state of the potential. Now, if the strength of the potential V is suddenly changed to 27, then the probability of the finding the particle in the ground state of the new potential, will be (upto two decimal places)

The value of the complex integral (zz) dz where C is the boundary of the half annulus (as shown in figure below), (upto two decimal places) is y 3 2 0 2 3

The magnetic dipole moment for the ground state of Cu nucleus as given by shell model is (upto two decimal placs), where is muclear magneton. Given g, 1. g, 5.59 for proton and g, 0 and g3.83 for neutron tr

Consider an ideal gas whose entropy is given by U 05 R ln 2R ln n where n number of moles, R universal gas constant, Uinternal energy, Vvolume, and constant. The value of the specific heats at constant pressure is nR(upto first decimal place)

A light beam is incident normally on an airdielectric interface. On reflection intensity of the beam reduced by 4. The dielectric constant of the dielectric is (Round off to two decimal places)

Consider a long solenoid carrying at a steady current. By suitable choice of guage transformation we can make vector potential zero. Only for inside region Only for outside region Both inside and outside region Neither inside nor outside

The Hamiltonian of a system is given by H k Px PyV(x,y) (where k is a constant). For what values of m and n, will the trajectory of system on xy plane be a circle Om 1, n 2 Omn2 Omn1 Om 2, n 1

Consider the following transformations A Q 2q 3p, P q 2p B Qp iq, P piq 2i (where i1) Which of the above is a canonical transformation Only A O Only B O Both A and B O Neither A nor B

In the circuit shown below, what is the value of transfer function II OZ 0 Z OZ Z 1 1 Z Z NN Z Z Lo

Consider a spinless particle of mass m moving in an infinite square well potential of width L i.e. V(x) 0 OVO L Ifa perturbation V, (x) AVL (x ) 1,is applied, the first order correction to energy of the 16 ground state will be O2AV L 8 O 42V L for

A twolevel system of N particles is distributed among two eigenstates 1 and 2 with eigenenergies E and E, respectively. The system is in contact with a heat reservoir at temperature T. If a single quantum emission into the reservoir occurs, population changes n1 and m m 1 take place in the system. For m1 and 1, the entropy change of the two

Given a system of two distinct lattice sites, each occupied by an atom whose spin (s1) is so oriented that its energy takes one of three values e1.0,1 with equal probability. The atoms do not interact with other. The ensemble average values for the energy U of the system, assumed to be that of the spins only, is O O 2 1e eB e e 1 e e e e 1ee

A parallel plate capacitor has circular plats of radius R and plate separation d R. The potential difference between the plates varies as V V sin cor. The total displacement current between the plates is O O VTR d sin cot Voco sin oot d EVR d Vow d cos cot cos cot

A charge particle q of mass m moving with a nonrelativistic velocity , enters into a magnetic field B at angle a. The power radiated by the charge particle is vB 6mc qvB cos a 6 mc qvB sin a 6mc3

A man at rest on a train that is moving with speed c4, shoots two bullets along opposite directions, each with a speed 3c4 with respect to himself as shown in the figure below. Which of the following options isare correct 3c 4 B 3c 4 (with respect to ground) Speed of A with respect to ground is 16c19 Speed of A with respect to ground is 13c19

A voltage signal 10 sin wt is applied to the circuit with ideal diodes, as shown in figure, which of following options isare correct Vin 10 www 4V 10k 4V In PHC V4V out In NHC V 7V out In PHC V7V out In NHC V 10V out Vout

Consider the integral b 1 (4x 3x 2). (x 5x4)dx, where a, b are constants. Which of the following options isare correct for the different values of a,b For a,b 0, , I 793 For a,b 1.5, , I 743 For a,b 0, 1.5, 1 53 For a,b 1.5, 2.5, I 0

A quantum mechanical system consists of onedimensional box of length L. Five identical noninteracting spin32 particles of mass m each are placed inside the box and the ground state energy of the system is found to be 32 eV. If Eo and E respectively denote the ground state energies when eleven such identical particles with spin32 are placed inside

Which of the following statements are correct for expression of density of states of nonrelativistic electrons In 3dimensional free electron gas, D(E) E. In 3dimensional free electron gas, D(E) E. In 1dimensional free electron gas, D(E) E. In 1dimensional free electron gas, D(E) E.

Choose the correct optionoptions from the following options. If a radioactive element disintegrates for an interval of time equal to its mean life, then the fraction that is disintegrated is equal to (e1)e. If 1 gm of Ra 226 has activity of 1 curie, then its halflife is 1581 years. The Actinium series starts from 92 U235 and ends at 32 Pb 208

Below given is the graphical representation of the production of ore of two companies A and B over the years (2001 to 2005) in million metric ton (MMT). 25 20 15 10 5 B 2001 2002 2003 2004 2005 Average production of ore of company A is what percentage of total production of company B over the years O 30 O 20 O 10 O 40

A man leaves his home and walks at a speed of 10 kmhr, reaching the bus stop 10 mins after the bus had departed. If he had walked at a speed of 15 kmhr, he would have reached the bus stop 20 mins, earlier. What is the distance (in km) from his home to bus stop O 15 O 20 O 10 0 12

A can do a work in 20 days, while B can do the same work in 10 days. A work for 4 days and B works for 5 days and leaves the work. The remaining work is done by C in 3 days. In how many days A, B and C working together can complete the work 04 O 6 03 05

What is the probability of being the sum of 9 from the throw of two unbiased dice 01 O O 12 1 6

Based on the patter followed in (I), and (II) find out what should come in place of question mark (2) in (III) 5 8 720 4 2 O 900 O 990 0100 O 984 2 120 (1) (III)

A photon of frequency 2mc h decrase in photon energy will be 3 scatters off a free electron of mass me by an angle The fractional (Upto one decimal place).

25x A 1D finite well of width a has a depth of V electrons that can be bound in this potential is 2 (m is electron mass). The maximum number of Sma Answer should be an integer.

3 The ground state energy when 12 noninteracting spin particles of mass m each are placed in a 3D isotropic harmonic oscillator of frequency o is O 20 w O 12 o O 16 o 0 26 o

A spherical shell of radius R, centered at the origin, has potential, for r R for r R Vo V VR The electrostatics energy stored in the system is VOR ARE VR VR VR

r In cylinderical coordinates, BT. The magnetic flux passing through the surface defined by 0.5 r2.5 and 02 2.0 is Wb. (Upto two decimal places).

An ideal gas (of adiabatic exponenty) is expanded so that the amount of heat transferred is equal to the decrease of its internal energy. The equation of state of the process is, then, given by TV(x1)2 constant TV(x2)2 constant TV(x1)4 TV(72)4 constant constant

The phase space trajectory of a particle of mass m in one dimension under an external potential V(x) and bounded between a and a is drawn as follows P The dependence of external potential V(x) on x is given by Ox2 Or 0x4

For a gas under isobaric conditions, its volume V varies with temperature I as VT32. The coefficient of (Specify your answer to two volume expansion is proportional to V. The value of n is places after decimal point).

Consider blackbody radiation in a cavity of volume V and temperature T. The entropy of the radiation depends on temperature as Tm. The value of m is (Specify your answer in integer).

The number of terms for the configuration 4d5d in LS coupling are integer). (answer should be an

For any two vectors and v, xv is solenoidal if O is solenoidal but is not O is solenoidal whereas is irrotational O and v are both solenoidal O and are both irrotational

If the trace and determinant of a 22 matrix are Tr(A) 4, Det (A)12 Then the eigenvalues of the matrix are O (3,4) (4, 3) O(6, 2) O (6,2)

Consider a radioactive nucleus that moves with a constant speed of 0.5c relative to the labouratory. The nucleus decays and emits an electron with a speed of 0.9c relative to the nucleus along the direction of motion. The velocity of the electron in laboratory frame is c. (in units of c). (Upto two decimal places).

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus ofradius R is given by 3 Z(Z1)e E 5 476 R The measured masses of the neutron H.N and O are 1.008665 u, 1.007825 u. 15.000109 u and 15.003065 u, respectively. Given that the radii of both the N and Onuclei are same, 1 u931.5 MeVc (c is the speed of light)

The fmax for an output amplifier that have a slew rate of 5Vus and a peak output voltage of 10V is (in kHz) O 34.92 O 64.80 O 79.6 00 R 1k0 N 5V V out

Which of the following is equivalent to the dual form of Y ABBCCA (A B) (B C) (C ) O (A B) (BC) (CA) O AB BCCA O(A B) (BC) (C A)

The maximum radius of the interstitial sphere that can just fit into the void between the body centered atoms of bec structure, is r. where r is the radius of atoms (Upto three decimal places)

In three dimensional two metals A and B have the number density of free electrons in the ration 12. The ratio of the cube of their Fermi energies is 023 012 014 041

A cylinder of radius R carrying current I. Now, if we make a cylinderical cavity of radius R2. The cross section has been shown in figure, and assume that the points P. O and O are in same straight line. The magnetic field at P will be P R HOI TR . (Upto two decimal places).

A plane electromagnetic wave, XE eot) after passing through an optical element emerges as 2x3E0 ) (kzcot) . The optical element is Quarter wave plate whose optical axis making 30 with xaxis. Quarter wave plate whose optical axis making 60 with xaxis. Half wave plate whose optical axis making 30 with xaxis. Half wave plate whose optical axis making

An electric dipole moment is placed at h distance above of an infinite thin conducting plane carrying o surface charge density as shown in figure, h x O The dipole will have only translation motion along 2 The dipole will have only rotational motion O The dipole will have both rotational as well as translational O None of the above are

For a gas of atoms of mass 2x1027 kg and particle density 6.410 m 3 at 50K, which of the following statistics is applicable Classical statistics Quantum statistics Either classical or quantum statistics Neither classical nor quantum statistics

A system of noninteracting spin half fermions with Fermi energy Ehas the density of states proportional to ENE, where E is the energy of a particle. The ratio of fermi energy and ground state energy per particle at zero Kelvin is (Specify your answer to one place after decimal places).

The first member of the principal series of sodium has a wavelength of 5893. The first excited S state of sodium lies 3.42 eV above the ground state. The wavelength of the first member of sharp series is A. (Upto two decimal places).

The moment of inertia of H molecule in rigid rotator is 2.5x 1048 kgm. If the average translational kinetic energy of an H molecule equal to the energy difference between the ground and first excited rotational states, then the temperature of H molecule is Kelvin..

The radioactive decay of two different nuclides are governed by the equations, dN dt dN dt N. 2 0.6 N N 0.3 If N (0)100, N (0) 0, then N (10) (Answer should be nearest integer)

The Laurent expansion of f(z) about z 1 is ze (z1) 2 ... e (z1) 2 (z1) 3 22(21)2(21 1 3 (1) 4.

The Hamiltonian of a system is given by P 1 2m 2 H kx 2x 3 If the phase space trajectory of the particle is an ellipse of eccentricity, e 2 frequency of small oscillations about stable equilibrium point is and m 1, then the angular (upto two decimal places)

Consider two inertial frames S and S with spacetime coordinates x,y,z,t and xy,z,t respec tively. Frame S moves along the xaxis with speed v relative to S frame. The origins coincide at t t0. An event occurs in S at x 9108 m and in S at x3108 m, t ls. The value of v is x108 ms. (Upto one decimal place).

Assume that a star has uniform density. The gravitational pressure P is related to volume Vas OV43 OV13 0213 13

Consider the springandmass arrangement below with no mass the spring has a rest length x.. Now, a mass m is introduced as shown in figure. Which curve in the gray box best represents the variation in total energy of this system FER x curve number1 O curve number2 curve number3 curve number4 m XX

Assume that famous scientist R. Feynman made a painting of purely carbon content. If weight of painting decreases by half when he visited it after 45 years of gap. The approximate age that the painting will survive 65 years 50 years 200 years 90 years

Consider secondharmonic generation of NdYAG laser pulses. A laser with Gaussian transverse profile operates at the wavelength of 1064 nm, the duration of the laser pulses is 10 ns (flattop), the pulses energy is 10 mJ with 1 KHz repetition rate, and the beam diameter 4 mm. The secondorder nonlinear susceptibility of the frequencydoubling crystal,

When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select correct statement about the directions of its angular velocity and angular acceleration. (A) Angular velocity upwards, angular acceleration downwards. (B) Angular velocity downwards, angular acceleration upwards. (C) Both,

You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting loca tion. Once you are airborne, you find that (due to a strong but steady wind) to maintain a northerly course you must point the nose of the plane at an angle that is 22 west of true north. From previous flights on this route in

The distance from New York to Los Angeles is about 5000 km and should take about 50 h in a car driving at 100 kmh. (a) How much shorter than 5000 km is the dis tance according to the car travelers (b) How much less than 50 h do they age during the trip

An astronaut must journey to a distant planet, which is 200 lightyears from Earth. What speed will be necessary if the astronaut wishes to age only 10 years during the round trip

For the circuit shown, find the Norton equivalent between the terminals a and b .

A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform vertical circular motion, under gravity. Minimum speed of a particle is 5m/s. Consider following statements. (P) Maximum speed must be 5?5m/s (Q) Difference between maximum and minimum tensions along the string is 60N. Select correct option: (A) Only the statement P is

For the triangle given below, state the law of sines and the law of cosines in terms of the angle measures A, B, and C and in terms of their corresponding sides a, b, and c. 6. State the Law of Sines A 7. State the remaining Law of Cosines abc2bc cos A (5 pts.) (5 pls.)

"A block of mass 2 kg is placed on a smooth horizontal surface and attached to a spring with a spring constant of 500 N/m. The block is pulled back 20 cm from its equilibrium position and released. If a frictional force of 4 N opposes the motion of the block, what is the maximum velocity attained by the block?"

A motor generates a torque of 5 Nm and has an efficiency of 80%. If the motor is used to lift a load of 200 kg to a height of 10 m in 10 seconds, what is the power output of the motor?

A motor runs at a constant speed of 5000 revolutions per minute and has a diameter of 10 cm. If the motor is used to drive a pulley with a diameter of 20 cm, what is the ratio of the torque delivered by the motor to the torque applied to the pulley?

A motor is used to drive a fan that produces an air flow of 5000 cubic meters per hour. If the motor has an efficiency of 75%, what is the power input required to drive the fan?

The left side of the manometer is open to the atmosphere (1.01 105 Pa) and the right side contains a gas with a gauge pressure of 50 Pa. The left side has a fluid with density 950 kgm. The remainder of the manometer has water (1000 kgm). The top fluid level is the same on both sides. What is the height of the column of low density fluid,Suppose

Refer to the op amp in Figure 1. If vi 0.5 V, calculate i. the output voltage Vo, and ii. the current in the 10 k ohm resistor.

For the op amp circuit in Figure 2, calculate the output voltage Vo.

For the circuit in Figure 3, calculate the Av and determine the output voltage Vo. Rf 10K, Rg 4K, VI 4 V.

A Second degree polynomial f(x) takes the following Valu.. f(x) 1x 4x2 .If integeral(2,0) f(x) dx is evaluated by following rule what is the error estimaton. 1) Trapezoidal 2) Simpson 13 rd 3) Simpson 38 not applied sub interval is 2.

Find the roots of the equation by bisection method upto 3rd approximation interval(2,3) f(x) x3 4x 9.

The Root upto 3rd approx. for f(x) xex 1 (0,1).

find the Root of equation using Rf method upto 2nd iteration f(x) xex cos x (0,1)

Using Euler Method find the approximate value of y corresponding to x2 given that dydx x2y and y(1)1 consider h0.1.

solve this dxdt 4t4, if xo0 at t0 fourth order delta t0.2.

Find the probablity of finding particle in the classical limit for ground state wave of harmonic oscillator.

Find out the probability of finding of electron in Hatom

Show directly by substitution into the EulerLagrange equations that changing the Lagrangian by adding a total time derivative of a function of the coordinates and time does not change the equation of motion L1(q, q,t) L(q, q, t) dFdt where F F(q, t). How is this consistent with the principal of extremal action (I have set this problem up for

Consider the electromagnetic gauge transformation A A VA and V V A t Show that this changes the Lagrangian exactly as in part (a), and therefore gauge trans formations do not change the equations of motion of a charged particle. What is F in this case

A cylindrical pressure vessel hold gas at an internal pressure of P 0.6 MPa, the inner radius of the tank is r 0.6 m, and the uniform wall thickness t 2 mm. The wall of the vessel is made of a material with a yield stress of Sy 350 MPa. 02. 01 02 01 (a) Calculate the hoop stress. (b) Calculate the longitudinal stress. (c) Calculate the

The peak in the 320380 nm portion of the UV absorption spectrum of pyridine shifts noticeably toward the blue portion of the spectrum on changing the solvent from hexane (C6H14) to methanol (CH3OH). The transition is

The mirror image between absorption and emission holds only when the excitation is between,

The 1HNMR of CH3F showed a doublet due to coupling of 19F. A 100 MHz NMR instrument has been used for recording the spectra. If the doublet signals appear at 4.525 and 4.075 ppm, the coupling constant (J) will be

show that the set of all rational numbers under addition is 9 group.

A proton NMR spectrum recorded in a 300 MHz NMR instrument exhibited a broad singlet at 12.48 ppm, two triplets at 3.12 and 0.94 ppm, respectively, and a pentet (quintet) at 1.78 ppm. The product is Option 1 Option 3 COOH COOH COOH x HC Option 2 Option 4 COOH COOH COOH

n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius ras shown in the figure. The masses of the mm balls are m respectively. What is 222 m 21 the minimum velocity which should be imparted to the first ball of mass m such that this nth ball will complete the vertical circle

In E. coli, oxidation-reduction reactions (or ATP hydrolysis) within the cell membrane generates a ?pH of 1.3 (interior higher by 13 unit) and a ?V of -121 mV (interior negative). Along with H+ ins, beta galactosides are cotransported in response to the total "proton motive force? How much energy (in kcal/mol) is made available by the above ?pH

The energy density I of a black body radiation at temperature T is given by the Plancks distribution function I(v,T)8piv2c3 hvehveknT 1, where v is the frequency. The function I (v,T) for two different temperatures T1, and T2, are shown below. 1 are, respectively, If the two curves coincide when I (v,T) is plotted against vT, then the values of a