Physics Questions and Answers September 30, 2022

From the set of equations p3q pr pr qs qt involving the unknowns of the ratio of t to r. qs p, q, r, s, and t, find the value

A highway curve forms a section of a circle. A car goes around the curve as shown in the helicopter view of Figure P1.48. Its dashboard compass shows that the car is initially heading due east. After it travels d 840 m, it is heading 0 35.0 south of east. Find the radius of curvature of its path. Suggestion You may find it useful to learn a

A negative point charge 10nC is situated at the origin (x, y, z) (0, 0, 0). What is the electric field intensity E at a point 5m from the origin (Write your answer in both spherical and Cartesian coordinates) Part II Calculate the electric field at point (x, y,z) (1, 3,1) due to a charge q1 10nC at (2, 1, 1). ( Dimension is in meters) Part III

A rectangular plate has a length of (21.3 0.2) cm and a width of (9.8 0.1) cm. Calculate the area of the plate, including its uncertainty. 36. How many significant figures are in the following num W bers (a) 78.9 0.2 (b) 3.788 x 109 (c) 2.46 x 106 (d) 0.005 3 37. The tropical year, the time interval from one vernal equinox to the next vernal

In the figure, the inner (shaded) region A represents a sphere of radius rA1, within which the electrostatic charge density varies with the radial distance r from the center as PAkr, where k is positive. In 2k PB the spherical shell B of outer radius r, the electrostatic charge density varies as dimensions are taken care of. All physical

In Circuit1 and Circuit2 shown in the figures, R 19, R 2 2 and R3 3 Q. P and P are the power dissipations in Circuit1 and Circuit2 when the switches S and S are in open conditions, respectively. Q and Q are the power dissipations in Circuit1 and Circuit2 when the switches S and S are in closed conditions, respectively. R www S R www. A B

A disk of radius R with uniform positive charge density o is placed on the xy plane with its centre at the origin. The Coulomb potential along the zaxis is (A) For A particle of positive charge q is placed initially at rest at a point on the z axis with z zo and zo 0. In addition to the Coulomb force, the particle experiences a vertical force F

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed about the vertical

T (D) If the surface of the bubble is a perfect heat insulator, then T P a2 Pal 4S 1 4S 1,A bubble has surface tension S. The ideal gas inside the bubble has ratio of specific heats y 3 bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is Pai, the radius of the bubble is found to be r and

(E) None

Area of the crosssection of a wire is measured using a screw gauge. The pitch of the main scale is 0.5mm. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below. Measurement condition Main scale reading 0 division Two arms of gauge

Which one of the following options represents the magnetic field B at O due to the current flowing in the given wire segments lying on the xy plane 1 L 2 42 (A) BHI (3 k 1 14 (1 2 2 ) k L 42 (C) BHI L2 L2 0 L4 3L4 L4 23 k (B) B ) k (D) B 1 HI (3 L2 22T Hol 140 ( 1 ) k L 4

By applying the first law of thermodynamics to isobaric process, obtain relation between two specific heats of a gas.

The OneSided SemiInfinite Potential Well (15 points) Consider a particle of mass m and energy E Vo, situated in a potential well that is infinite on the left wall (at x 0) and a finite height Vo on the right wall (at x L). O 0, write down the form of the wavefunction inside the well (a) Noting the boundary condition at x (i.e., for 0x L), in

Consider the finite square well potential shown in the following diagram E0 The potential is given by 0 11 U(x) 0 U for x 0, xL 1U for 0 L write down the four equations arising from the boundary conditions that apply at x0 and xL. d) By eliminating C and D from these equations show that

Mature salmon swim upstream, returning to spawn at their birthplace. During the arduous trip they leap vertically upward over waterfalls as high as 3.35 m. With what minimum speed (in m/s) must a salmon launch itself into the air to clear a 3.35-m waterfall? ________________ m/s

In a group of 15 people, 7 read French, 8 read english while 3 of them read none of these two. How many of them read French and english both 0 3 4 5

In a triangle ABC, BD is bisector of LABC and ZDBC 60. What is the length of BD,B D a Ocb cb cb bc c b (bc) be

The group velocity (v) and phase velocity (vp) of a wave packet obeys vgVp c, where c is a constant. If co (k 0) 0, then which of the following expresses the dispersion relation for the wavepacket (0) k,A k n Am Ark k

Consider two ultrahigh speed drag racers. One drag racer has a red stripe on the side and overtakes the other drag racer at a relative speed of 3c2. If the red stripe has wavelength 635 nm, then the wavelength of the stripe as observed by the other drag racer is nm. (correct up to one decimal places)

The moment of inertia of a uniform elliptical plate of mass 4 units having semimajor axis 5 units and semiminor axis 1 unit, about an axis passing through its centre of mass and perpendicular to its plane is units. (Answer should be an integer)

15 electrons are in a potential V(x, y), where V (x, y) mos (x y). The degeneracy of the level containing the most energetic electrons is (Answer should be an integer)

Consider a system of two ising spin S, and S, taking value 1 with interaction energy, JS,S, in thermal equilibrium at temperature T. The number of configurations corresponding to ground state energy of the system is (Answer should be an integer)

Consider a Hydrogen atom in the state n 2. 1, m0 the value ofr at which the radial probability density of the hydrogen atom reaches its maximum is a. (Answer should be an integer) Given R(r) 1 (26a5) rer2a0

In the Laurent series expansion of f(t) z1 (answer should be integer). 1 22 valid in the region z2, the coefficient of is 22

A pion decays from rest to give a muon of 3.57 MeV energy in a reaction, uv. The kinetic energy of the associated neutrino is MeV (upto two decimal places) Given m 273 m. m 207 m, and m 0.51 MeVc

According to Josephson effect if we apply a static potential V across the junction it leads to the production of alternating current. If the value of V is 10 mvolt. The frequency of the current will be x102 Hz (answer should be upto second decimal place)

The value of the commutator bracket Lx Ly. L. L will be equal to i (Lx Ly) i (L Ly) 2i (Lx Ly) O2in (Lx Ly)

Let P (a) be a 5 5 matrix such that aj be smallest and largest eigenvalue of P. If a B 14.5, then b is 01 0 for i j otherwise a b , wh (75) where b0. Let a and B 1

The ratio of the intensity of the polarized component to the intensity of the unpolarized component is 0.25 of a partially polarized light. The degree of polarization of this light is 0.1 0.2 0.3 0.4 4

Which of the following nuclear reactions is not forbidden n P nk k pe 5 Oute 5

A uniform charged sphere of radius a and carrying the charge density and spinning at a constant angular velocity about zaxis. The current density at any point (r.0.) inside the sphere is given by O poro por sin e por cos 06 po cos p

In a 4bit DA converter the full scale output voltage is 5V. Its resolution is approximately O 0.3 V O 1.25 V O 0.5 V 0 2.5 V

In carbon atoms which of the following terms will have minimum energy D 03 P2 3 Po 050

Which of the following molecule is rotational, vibrational, Raman and NMR active 12C160 O HH H5C1 O6C16N

A twodimensional lattice has basis vectors, a 2 and b i 2j. The basis vectors of the receiprocal lattice are a 7 and b 7 b a r a and b j and b 7 j a 1 and b j j

The length element ds of an arc is given by The metric tensor gi is 5 3 5 1 3 54 54 1 3 0 1 52 3 52 1 (ds) 3 (dx) (dx) 5 (dx)(dx)

The Lagrangian of a system is given by 4crr rw ) mgcr. 2 L 1 (p.2. 2 Where c. co., m. g are constants. If r(t 1) and r(t 1) 0, then the radial acceleration at 1 1 will be, 5 5 el T C g 5 2c 1(23) (228) 2g 5 2c g 1

For a particle of mass m moving in the potential V(x) mox, a small perturbation H x is applied only for positive x, A0 being a constant. The first order correction to ground state energy is 0 2 mo. mos K mo 2 2

The spinstate wavefunction of a particle is given by 1 x) 2i 3i In standard basis If a beam of No such particle is sent through a SternGerlach apparatus with a magnetic field alongzaxis, then the number of undeflected particles will be equal to (Consider No to be very large) O No7 02N07 03N7 Zero

W NC (TT) W NC (TT) 0,Two identical bodies have internal energy UNCT, with a constant C. The values of N and C are same for each body. The initial temperatures of the bodies are T, and T. and they are used a source of work by connecting them to a Carnot heat engine and bringing them to a common final temperature T. The work delivered is W NC (TT)

The entropy of a gas containing Nparticles enclosed in a volume Vis given by SNkg In , where E is the total energy, a is constant and k, is Boltzmann constant. The chemical potential of the system at a temperature Tis ukT In ukgI In ukgT In u kgI In aVE 32 N52 aVE 32 N512 aVE 32 NS12 aVE32 NS12 aVE32 NS12

If y(x) is a particular solution of y sinx(y)2ye and y(x) is a particular solution of y sinx(y) 2y cos 2x then a particular solution of y sinx(y)2ye 2 sinx is given by (x) y(x) 1 y (x) (x) 122 O p(x)y(x)1 Oy(x)(x)1

If Y (p) is the laplace transform of y(t), which is the solution of the initial value problem y(t) dt p1 1p sin t satisfying y (0) 1 and y(0)0, then the Y(p) equals P 2p 1p (1p) 32 P e2pm 1p (1p) p(1p)1 (1p) 0 2

Let A, A, by P(4,)117, a a Abe n independent events and the probability of occurence of the event A, is given a 1, 1, i 1, 2........, then the probability that at least one event occurs is 158 1 n(n1) 2 1 n(n1) 2 (14)

O 216 86 Rn,The binding energy of a nucleus with atomic number z and atomic mass number A is given by semiempirical mass formula B(2. A)a4b43c(42) where, a 15.8 MeV. b 18.3 MeV, c 23.2 MeV. d 0.7 MeV and 6 (11.2, 0, 11.2) MeV for nuclei which are (oddodd, oddeven, eveneven). If we consider all possible isobars of mass number 216, the most

Suppose a plane EMwave with electric field x10 cos (kzcot) Vm is incident from air on a dielelectric occupying the region z 20. Assuming that the permitivity of the medium is 48 and permeability, the electric field of the reflected waves can be written as E x cos(kzcot) 10 xcc x cos(kz cot 10 xcos (kz cot) 3 20 xcos (kz cot) 3

Consider a dielectricconductor interface at z 0. The magnetic field in the dielectric z 0 is given by H jH cos kz cos cot, then the surface current density is given by xH sin cot xH cos cot H sin cot O cos ot

(a La 125 (2) 4 d Let (z2)4 ( 01i O 2 2i 03i 04i dz 47i, where the closed curve C is the triangle having vertices at i, the integral being taken in anticlockwise direction. Then one value of a is

The output of the given circuit is (assume that the diode is ideal) Vin C F 10 10 O 13V TV 3V T pac 23V 10V t 0 t R Vo,Vo 10V 3V A t

If the given circuit behave like mod10 counter the inputs of NAND gate will be Q3 Jo CLK Supply voltage KOCIO 20 and 23 Q and Q3 O Q and Q3 Qo and Q LSB J KIC J Q KCr K3CrQ3 MSB

The transition J 3 to J 4 in HCI molecule is associated with radiation of 83.03 cm1. The transition J10 to J 11 occurs at 100.65 cm1 228.36 cm1 300.14 cm1 O 19.82 cm1

The DrudeLorentz formula for the dielectric constant of a solid is 0 0 0) ior (0) 1 Here is the plasma frequency, is the energy gap for interband transitions and r is the scattering time of the electron. At room temperature the value of r of copper is 1014 sec. The value of plasma frequency op is 01.2106 Hz O 1.6x106 Hz O 2x106 Hz 2.4106 Hz

Spacecraft A is moving at 0.90c with respect to the earth. If another spacecraft B is to pass A at a relative speed of 0.50c w.r.t. A in the same direction, then the speed B must have (in units of c) with respect to the earth is c (up to two decimal places).

A particle is described by a wavefunction y (r. ) A er12 ( r If L is measured, then the probability of finding is sin cos o sin (Answer upto one decimal place)

Consider scattering of particles of mass m and energy E from the Yukawa potential. V(r)g (g and u are constants) In the limiting case u 0, the differential scattering crosssection at an angle will be equal to 8 2 8 (a b) ax (g4E). (Answer should be an integer) Given ex sin bx dx

Two thermally isolated identical systems have heat capacities which vary as C BT (where 0). Initially one system is at 300K and the other at 400 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. The final temperature of the combined system is K.

In weak magnetic field the number of spectral lines observed in the transition (D P) will be (answer should be integer)

Assume that E vs k relationship for electron in the conduction band of a hypothetical tetravalent ntype semiconductor can be approximated by E ak constant The cyclotron resonance for electrons in a field B 0.1 Wbm occurs at an angular rotation fre quency1.8x101 rad s1. The value of a is 1038 Jm (upto first decimal place)

A plane polarised light wave with electric field expressed as (z,t) Ej cos (kz cot) is incident from the left on the apparatus as sketched below. Left Y 4 X Fast axis YI 3 P Z Right I w.r.t. the yaxis, The apparatus consists of (from left to right) a polariser with transmission axis at followed by a quarterwave plate with fast axis along the

Which of the following isare NOT linear operators Ap(x)do Ap(x) Q(x)x Ap(x)dokp(x) Ap(x) g(x) kx

The wavefunction of an electron in an eigenstate of a Hydrogen atom is given by 32 1 1 r LAD (2) exp cos ao ao 240 y (r,0,0) 4 r where ao is the first Bohr radius. Which of the following statement(s) isare CORRECT The energy of the electron is (3.4 eV),The energy of the electron is (1.51 eV) Expectation value of L for the given state will be 2

(AN) (AE) (AE),Consider a system consisting of indistinguishable and noninteracting particles obeying classical statistics. Each particle can exist in only two states, one with energy and the other with energy . The grand canonical partition function of the system is given by ZN (,) N0 N aN 1 where, Z Z (B) is the single particle canonical

Consider a solid sphere of radius R with uniform volume charge density Po. A very narrow tunnel is drilled along the diameter of the sphere. A point charge q and mass m is released at the edge of the tunnel (point A in the figure). Assume that charge on the sphere is not able to move). Which of the following statement(s) isare correct

Gold is monovalent metal with molar mass 197 gmol and density 19.3 gcm. the electron density (electron concentration per unit volume) is 3.9 1028 m. the Fermi energy of gold at 0 K is 3.5 eV. the electron density (electron concentration per unit volume) is 5.9 x 1028 m. the Fermi energy of gold at 0 K is 5.5 eV.

Consider a consumer who is deciding to buy insurance for his beachfront house. Suppose the probability that the house will get damaged by the rising sea level is 0.4. Let us assume that the valuation of the house is 100 (in thousand dollars) and in case of a natural calamity due to rising sea level, the valuation of the house would become 40. At

Compute the relative concentration of silicon atoms and electronhole pairs at 300 K. Also, calculate intrinsic resistivity of silicon. Given Avogadros number 6.02 x 10 atoms gatom, density 2.33 x 10 gm, atomic Wt. 28.1, intrinsic carrier density 1.5 x 10 m H 0.14 mVs. p 0.05 mVs.

Newton's Second law of motion states that equation below: Sum of F = ma where Sum of F is the total external force acting on the body, m is the mass and a is the acceleration of the body. Describe Newton's second law in terms of change in the momentum. 1) The sum of all external forces acting on the object is equal to the object's change in

A lap joint is constructed as shown above with 2 rivets holding together the 5 plates shown. Determine the required diameter, dreq, to the nearest 18, of each rivet if the stack of plates is in equilibrium. Take P 1.50 1000 lb and assume that the rivets are manufactured from 2014T6 aluminum. Also take the thickness of each plate to be . Make sure

Two currentcarrying wires are located 12.5 cm apart, as shown below. The wire on the left card p current of 562 mA out of the page and wire on the right carries a current of 378 mA into the page. Point P is 8.7 cm directly above the right wire. What is the magnitude and direction of the magnetic field at Point P Express the direction as an angle

A train with crosssectional area S, is moving with speed v, inside a long tunnel of crosssectional area So (So4S). Assume that almost all the air (density p) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its

A point charge q of mass m is suspended vertically by a string of length 1. A point dipole of dipole moment p is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing

A beaker of radius r is filled with water refractive index (1) in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed co. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is h(h H, h

A student skates up a ramp that makes an angle 30 with the horizontal. Heshe starts (as shown in the figure) at the bottom of the ramp with speed vo and wants to turn around over a semicircular path xyz of radius R during which heshe reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is

A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed o about the pivot. The maximum angular speed M is achieved for x XM. Then (A)

In an Xray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission I of continuous and characteristic Xrays. If the filament current I is decreased to, the potential difference d V is increased to

Two identical nonconducting solid spheres of same mass and charge are suspended in air from a common point by two nonconducting, massless strings of same length. At equilibrium, the angle between the strings is a. The spheres are now immersed in a dielectric liquid of density 800 kg mand dielectric constant 21. If the angle between the strings

Starting at time t 0 from the origin with speed 1 ms, a particle follows a twodimensional trajectory in the xy plane so that its coordinates are related by the equation y The x and y components of its 2 acceleration are denoted by a, and ay, respectively. Then (A) ax 1 ms implies that when the particle is at the origin, ay 1 ms (B) ax 0

A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be po. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (Ra). For a R the magnitude of the work done in the process is given by (4rpoRa)X, where X is a constant and yCCy4130. The value of X is

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance R3 has temperature coefficient 0.0004 C. If the temperature of R3 is increased by 100 C, the voltage developed between S and T will be volt. R6052 www 50V SR330092 www V P R10002 www R450092 T www

Two capacitors with capacitance values C 2000 10 pF and C 3000 15 pF are connected in series. The voltage applied across this combination is V 5.00 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is

dP A cubical solid aluminium (bulk modulus V 70 GPa) block has an edge length of 1 m on the dV surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10 kg m and 10 ms2, respectively, the change in the edge length of the block in mm is

The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the selfinductance of the inductors, resistances, mutualinductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced EMF in the

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm and it is absorbed by the water over an effective area of 0.05 m. Assuming that the heat loss from the water to the surroundings is governed by

Consider the following compounds in the liquid form O2, HF, HO, NH3, HO2, CC14, CHC13, C6H6, C6H,Cl. When a charged comb is brought near their flowing stream, how many of them show deflection as per the following figure

In the chemical reaction between stoichiometric quantities of KMnO4 and KI in weakly basic solution, what is the number of moles of I released for 4 moles of KMnO4 consumed

An acidified solution of potassium chromate was layered with an equal volume of amyl alcohol. When it was shaken after the addition of 1 mL of 3 HO, a blue alcohol layer was obtained. The blue color is due to the formation of a chromium (VI) compound X. What is the number of oxygen atoms bonded to chromium through only single bonds in a molecule

20. In a crystalline material, planes of symmetry are labeled using triplets of integer numbers of the form (hkl), e.g. (100) is equivalent to h 1, k 0, 1 0. For this question it is not important how this labeling scheme works exactly or what h, k and I mean. By performing certain experiments, it is possible to determine these (hkl) triplets

Consider the above circuit. The filament lamp A consumes an electrical power PA 100 W when it alone is connected to a voltage of U 100 V. Filament lamp B consumes a power PB 20 W when it alone is connected to a voltage of U 100 V. (a) When the switch is closed, which lamp will be brighter and why Find the ratio of the levels of brightness of

18. The diagram shows two spheres of mass m suspended from wires of negligible mass. The length between the pivot points and the centres of each sphere is L. The two suspension points lie on a horizontal line and are separated by a distance z. The system is in equilibrium. Take the total acceleration due to gravity to be g. Hint You may assume

Consider the cross section of a pencil, where a concentric circle of radius r sits at the centre of regular hexagon. If the black area is a quarter of the total area of the hexagon, what is the length of the dimension r in terms of r X 2r 6

A car is initially stationary. At time to it starts to move at speed v for a time At. Immediately after this it moves at speed u for a time At At. After this time it is stationary again. (a) Using this information sketch a graph of speed u versus time t. Label all axes sufficiently so that the graph is quantitatively accurate. (b) From your

Consider the network of capacitors shown below. All capacitors in the network have the same capacitance C. Assume that capacitances combine as follows Two capacitors in series combine their capacitance in the same way that two re sistors in parallel combine their resistance. Two capacitors in parallel combine their capacitance in the same way

A light ray passes through an infinite stack of thin transparent plates. The refrac tive index of these plates increases slightly by a constant factor from one plate to the next. The ray enters the first plate making an angle o with the surface normal. The rays angle to the normal changes at each new interface. At the ith interface between plates

A rectangular building with sides 50 m and 100 m long has a flat roof on top of it. The roof has a mass per unit area of 100 kg m2. The walls are 10 cm thick and can take a maximum stress of Smax which depends on the material of the wall. The values of Smax for five building materials are moist wood Smar 25.5 Nmm dry wood Smax 48.3 N mm2

The sketch below shows a ball of mass m on a spring of unextended length Ro and spring constant k. The spring is pivoted on the left on a central axis marked with a cross. The axis is perpendicular to the plane of the sketch. The ball and spring rotate around the central axis on a smooth horizontal table as indicated by the arrow in the sketch.

A conical cup has dimensions as shown in the diagram of its crosssection below. The cup can hold a maximum volume V when filled to its full depth H. Find an expression for the depth h to which you have to fill the cup so that it contains a volume of liquid equal to V2. Your expression for h should only depend on the dimensions of the cup. D H

21. You wish to build an adjustable delay line using electrical switches as shown in the diagram below. L 1 L1 I L1 Its purpose is to adjust the delay of an electrical signal through the delay line by switching different amounts of delay into the signal path. The delay line should use the minimum amount of switches. The delay line should have a

The diagram below shows an interferometer with two paths (Path A and Path B) which a wave can take from its source S to a detector D. Source S Path A Path B Detector The lengths of the paths differ by an amount L which can change with time. The intensity at the detector I is measured and varies as a function of L as follows I Ip I, cos(kL) In