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Physics Questions and Answers November 02, 2022

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Electric field and magnetic field in a region are kxty and B The current density in the region is Ok z (x z) k 0 z (x z) koxz 2c Ok 1023) (x y ) .

The electric field of an electromagnetic wave in ret frame S is yE (). This same wave is observed from an inertial frame S moving in the xdirection with velocity with respect to .S frame. The intensity of light in S frame will be 01 OCE ocE 03 EOCE 3 10 EOCE

A wire loop of radius R carries alternating current I(t) I, cos (cot). The loop is placed in xz plane as shown in figure. Consider three points P, Q and R at the same distance from origin on the x, y and zaxis respectively. If the intensity of at radiation P, Q and R are Ip. I and I respectively, then X P Z OR IpIQ IR O IpIR IQ Ip IR IQ O IpIR

A electron is released from rest from height h and falls under the influence of gravity. The fraction of the potential energy lost in radiated away when it reach to the ground is (m and e are mass and charge of electron) g Vh 2g V h h ool (2g h

Given the scalar and vector potential in free space o(r,t)0 A(r,t) A, sin(kxcot) where, A, k and are constant. The time average of the poynting vector is given by O iwokA 2440 Oiok4 2440 O jok4 2440 O jookA 2

When a charge particle approaches to a conducting grounded surface, radiation is emitted, associated with the changing electric dipolemoment of the charge and its image. If the particle has mass m and charge q, the ratio of total emitted power when charge particle at a distance 2z and z respectively from the plane, is,041 014 012 0116

Suppose in the rest frame we have, Ex , B, B y Now, we go to a frame moving with velocity V Vox The nonzero components of E and B in the new frame are OE, E,, B, and B, O Ex, E, and B, OE,, B, and B. OEx, E,, B, and B.

The vector at(xjy), a (x y) where a is a constant and t is time. The electric 6 field (E) and magnetic field (B) corresponding to these potentials are, respectively a(xy)(xy), atk Oa(xy)i (xy)i. at k 012a xiy, at k 1a(xy)(xy), at k

An electromagnetic wave E 20 e is travelling in isotropic linear nonmagnetic dielectric medium. The dielectric constant (,) of the medium is 3 9 (4x3y510) Vm 5 03

The instantaneous electric and magnetic fields created at a distance r by a point source at the origin are given by B cos cot Hor Acos cot where The timeaveraged power radiated by the source is DE 08 AB Ho 2 , A, B are constants, and the unit vectors (1,0, 6) form an orthonormal set. AB Oc AB C H AB

A charge particle with charge q moves with constant velocity v along zdirection. Its scalar and vector potentials are 9 V (1)(xy)(zvt) and where Both V Neither These potentials define electromagnetic waves under Coulomb Gauge only. LorentzGauge only. and c is speed of light.

A uniform magnetic field B Bok. Now a particle of charge (q) and mass (m) is thrown from the point 2mvo qBo 0. 0 with initial velocity voi. The minimum time it will take to reach origin is O m qBo 2mm qBo 3m qBo O it will never reach

A nonconducting circular dies of inner radius a and outer radius b, Q charge is distributed on the disc. The disc is rotating about it axis with angular velocity. The magnetic field at centre of the disc is MowQ (ba),( 0p zq) 1 n T(ba) O 2 O r (b a n

A regular hexagonal loop of wire having sides a carrying current is bent into a bookend shaped loop (two perpendicular planes) of two equal parts. The resultant magnetic field at the centre will be 2 2

Three infinitelylong conductors carrying currents I, I, and I lie perpendicular to the plane of the paper as shown below. If the value of integral Bde for the loops C, C, and C, are 2. 4 and units of NA, respectively, then C 1 0 1 0 O 15A into the paper into the paper O I 3A 1 O I3 14 out of the paper

A square loop (of conducting wire) of side a and resistance R is being rotated about a vertical axis as shown in the figure. A uniform horizontal magnetic field of strength B passes through the loop. If the frequency of rotation is v. The average power dissipated in the loop is a 22 Bav 4R 42 Bav 2R 0 2 Bav R B

The magnetic vector potential (A) inside a long wire of radius R is given by Aks2. Where s is the distance from the axis of the wire. The current density (1) inside the wire at a distance s from the axis is O O 4k Ho 2k Hos 1 Hos 2k N 2 Mos z

A non conducting circular dise of radius R has uniform charge Q distributed on its surface. It is rotated about its axis with angular speed. Its magnetic moment is QOR QOR 2 2Q0R 3 O QOR 4

The region at space z 0 and z0 are filled with materials having permeability 2140 and 440 respectively. The magnetic field in the region 2 0 is B 40 (15x30y 452) and there is a surface current distribution k10x Am at z 0. The magnetic field in the region z0 is Ho (70x60y452) O 140 (30x20y452) O Ho (70x20y452) O Ho (30x20452)

A current loop ABCD is held fixed on the plane of the paper as shown in figure. The arcs BC (radius) and DA (radius7) of the loop are joined by two straight wires AB and CD. A steady state current I is flowing in the loop. Angle made by AB and CD at the origin O is 45. The magnitude of magnetic field (B) due to the loop ABCD at the origin (O) is I

An infinitely long wire passing through origin (0, 0, 0) is carrying current lo lies along xaxis. The magnetic field at the point (2, 3, 4) will be Io(2i 3j 4k) Molo 50 (4j3k) 50 (4 2k) 50 (2j31) (23i) 50

The volume current density through a long cylindrical conductor is given to be J J,212 where, R R is radius of cylinder and r is the distance of some point from the axis of cylinder and J is a constant. The value ofr at which magnetic field maximum is O 3R 2 2 3R 4 R 4

A long thin wire carrying a current I lies parallel to and at a distance d from a semiinfinite slab of iron d of infinite permeability u as shown in the figure below. The magnetic field at 00 TAXRE 111 y d 440 I 2 3nd I AHOI(2) 3nd 201 2 3nd 0 24 (2) 3nd is

A long current carrying wire is bent into a curve as shown in figure. (Assume that the linear portion is infinitely long and curve portion is a semi circle of radius R. If wire carries current lo, then magnetic field at O is 4R (11) 1 4R L H (11) Molo ( 2R (11) OM (11) 2R I

A metallic rod of length is rotated about its one end with uniform angular velocity o such that the axis of rotation is perpendicular to length ofrod. There exists a uniform magnetic field B parallel to axis of rotation. Potential difference between free end center of rod is O Bol 2 O Bol 4 3B01 8 O Bol 8

A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. The magnitude of the magnetic field at the point P is given by P O 1 124 Ja 2a 3 Ho Ja 5 1212127144 O 1 Ho Ja 3 Ho Ja a

A long solenoid of radius r and the number of turns per unit length n is driven by an AC current i I sin cot. Now, a small circular loop at radius a and resistance R is placed coaxially inside the solenoid. The induced current in the loop is given by gnIo sin(t) R nlocos(t) R R cos(cot) nlo R sin (cot)

A current carrying wire is placed in uniform magnetic field as shown in figure. The magnetic force acts on the wire is B.() X (x) (x) T X X X (X) X (X) (x) (X) (x) L by (x) X O2(LR) Boloj (1 2 (LR) Boloj,01 (LR) Boloj (LR)Boloj 2

A laser operating at 600 nm is used to excite a molecule. If the Raman shift is observed at 750 cm1, the approximate positions of the antistokes and the stokes line are, respectively 574.16 nm and 628.27 nm 525 nm and 675 nm 574.16 nm and 750 nm

An AC mains line has frequency 50 Hz, and an amplitude of220V, to which a DC voltage of 20 volts is added, so that the voltage swings between 240 to 200 V. find i) average value (2marks,ii) meansquare value (3marks,iii) rootmeansquare value (1marks),b) Give signal interpretations for the following statistical averages i) X(t) (1mark),ii) X(t)

provide noise model for a resistor R, based i) Norton equivalent circuit (2marks),ii) Thevenin equivalent circuit,b) Give a suitable definition of available noise power. Then show that for resistance Rs the available thermal noise power spectral density S(Pa) is given by S(Pa) kT where k is Boltzmanns constant and T is temperature in Kelvins.

Sketch suitable diagrams showing the following interference coupling modes for two circuit blocks and indicate the area of vulnerability i) common mode (3marks),ii) differential mode,antenna mode,b) Discuss the following grounding techniques and where they are most appropriate i) single point grounding (4marks),ii) multipoint grounding,iii) hybrid

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R100, R60 and R40, respectively, the relation between these resistances is 1 A) 1 1 R100 R40 R60 C) R100R60 R40 B) R100 R40 R60 D) 1 1 1

To Verify Ohms law, a student is provided with a test resistor RT, a high resistance R, a small resistance R, two identical galvanometers G and G, and a variable voltage source V. The correct circuit to carry out the experiment is A) B) C) G www R RT z R G www RT tra G M R www R D) G R RT G R RT 412 G R www R

An AC voltage source of variable angular frequency and fixed amplitude V, is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When oo is increased A) the bulb glows dimmer B) the bulb glows brighter C) total impedance of the circuit is unchanged D) total impedance of the circuit increases

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is X X X A) IBL IBL C) X X X XXXX X

A block of mass m is on an inclined plane of angle 0. The coefficient of friction between the block and the plane is and tan 0 . The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P mg(sine cose) to P mg(sine cose), the frictional

A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is A) C) 2GM (425) 7R GM 4R 3R B) P B) 4R 4R 2GM (425) 7R 2GM (21) 5R

Consider a thin square sheet of side L and thickness t, made of a material of resistivity p. The resistance between two opposite faces, shown by the shaded areas in the figure is A) directly proportional to L C) independent of L B) directly proportional to t D) independent of t

A real gas behaves like an ideal gas if its A) pressure and temperature are both high B) pressure and temperature are both low C) pressure is high and temperature is low D) pressure is low and temperature is high

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms. Which of the following statement(s) is (are) correct for the system of these two masses A) Total momentum of the system is 3 kg ms B) Momentum of 5 kg mass after collision is 4

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is Po. Choose the correct option(s) from the following A) Internal energies at A and B are the same B) Work done by the gas in process AB is PoVo (n 4 C) Pressure at C is Po 4 D) Temperature at C is To 4 VA 4Vo Vo C To B A T

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true A) Error AT in measuring T, the time period, is 0.05 seconds B) Error

A few electric field lines for a system of two charges Q and Q fixed at two different points on the xaxis are shown in the figure. These lines suggest that A) QR B) QQ C) at a finite distance to the left of Q, the electric field is zero D) at a finite distance to the right of Q the electric field is zero

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60 (see figure). If the refractive index of the material of the prism is 3, which of the following is (are) correct A) The ray gets totally intemally reflected at face CD B) The ray comes out through face AD C) The angle between the

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T.(0). An interesting property of superconductors is that their critical temperature becomes smaller than T.(0) if they are placed in a magnetic field, i.e., the critical

If the total energy of the particle is E, it will perform periodic motion only if A) E 0 C) VoE0 B) E 0 D) E Vo,When a particle of mass m moves on the xaxis in a potential of the form V(x) kx it performs simple harmonic motion. The corresponding time period is proportional to as can be seen easily using dimensional analysis. However, the motion

For periodic motion of small amplitude A, the time period T of this particle is proportional to A) A B) C) LOLE D) A m,When a particle of mass m moves on the xaxis in a potential of the form V(x) kx it performs simple harmonic motion. The corresponding time period is proportional to as can be seen easily using dimensional analysis. However, the

The acceleration of this particle for x X, is A) proportional to Vo C) proportional to V mX B) proportional to D) zero Vo mXo,When a particle of mass m moves on the xaxis in a potential of the form V(x) kx it performs simple harmonic motion. The corresponding time period is proportional to as can be seen easily using dimensional analysis.

Gravitational acceleration on the surface of a planet is 6 g, where g is the gravitational acceleration on 11 the surface of the earth. The average mass density of the planet is times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms, the escape speed on the surface of the planet in kms will be

A piece of ice (heat capacity 2100 J kg C and latent heat 3.3610 J kg) of mass m grams is at 5C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the icewater mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

A stationary source is emitting sound at a fixed frequency fo, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2 of fo. What is the difference in the speeds of the cars (in km per hour) to the nearest integer The cars are moving at constant speeds much smaller

The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in m25 front of it to 50 cm, the magnification of its image changes from ms to m50. The ratio is m50

An a particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are and 2, respectively. The ratio, to the nearest integer, is Na

When two identical batteries of internal resistance 122 each are connected in series across a resistor R, the rate of heat produced in R is J. When the same batteries are connected in parallel across R, the rate is J. If J 2.25 J then the value of R in 22 is

Two spherical bodies A (radius 6 cm ) and B(radius 18 cm) are at temperature T and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross sectional area is 4.9 x 107 m. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s. If the Youngs modulus of the material of the wire is nx 10 Nm, the

A binary star consists of two stars A (mass 2.2M) and B (mass 11M), where M, is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

What is a Building and Building Services?

what are the Main objectives of building services design engineering?

Explain the STRUCTURAL BUILDING COMPONENTS

(21)3 ((100)x)12, the value of x ............. 05 06 07 None of these

A zener diode is operated in breakdown condition as shown in the circuit. If the range of IL (load current) is 5mA 13 mA. The value of Iz(max) is 1K I A 25V 5 mA 8 mA 13 mA none of these 12V I R

If the diode in the given circuit shown below is ideal. The current lp will be,25V 15 0 mA 0.5 mA O 1 MA O 2 mA 10k I 20V 4

A particular green LED emits light of wavelength 5490 . The energy band gap of the semiconductor material used there is (Planks constant 6.626x1034 Js), 2.26 eV O 1.98 eV O 1.17 eV O 0.74 eV

Consider the circuit shown in the figure below 6V R 2 3 R R Let the value of V. be equal to 3V and output voltage be equal to 9V then value of R 0.33 O 0.5V R V will be

The circuit shown in figure is excited by the input waveform shown (Assume all the components are ideal). FA Fo O The wave form of the output Vest IV 0.5 O Vast 4 0.5 0.5 V V IV IV A 0.5 HH t(sec) t(sec) t(sec) t(sec) V.

For the curcuit in the figure, the voltage vo is ww www 292 292 4V 2V O 1V O1V None of these 202 2V

In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5V across RL, the minimum value of R in ohm and the minimum power rating of the Zener diode in mW, respectively, are 10V 100 V5V 125 and 125 125 and 250 250 and 125 250 and 250 Load R

5V O out Vout 5V t J,If the diodes shown in circuit given below are ideal, then the output waveform is SV SV O in A V out 5V 5V V out 5V r Vin D XXX D t out

The voltage V and V of the arrangement shown in figure (Assume diode cutin voltage V 0.6V) 6Vo 6V and 5.4V 5.4V and 6V 3V and 5.4V 6V and 5V D 6V 10 D 310 k 63V V V

A body moves with velocity u ac, where c is speed of light and 0

Suppose that a particle moves relative to O with a constant velocity of c2 in the xyplane such that its trajectory makes an angle of 60 with the xaxis. If the velocity of O with respect to O is 0.6c along the xx axis, then the equations of motion of the particle as determined by O are Ox0.74 ct, y 0.43 ct Ox0.30 ct, y 0.74 ct,O x 0.74 ct, y

A square of area 100 cm is at rest in the reference frame S. An observer in S frame which moves relative to S at 0.8c and parallel to one side of the square measures the area. The area measured by observer is S frame is 80 cm,60 cm O 166.67 cm 0125 cm

An unstable particle travels a distance of 900 m in lab frame. Kinetic energy of the particle is 25 of rest mass energy. Proper life time of the particle is 0 2.2510 sec 0410 sec 06.2510 sec 08x10 sec

Consider a dynamical system, defined by a set of equations (in terms of q and p canonical variables) qqp pqp For this system, the Hamiltonian is, 1 q O HPq 2 2 OHqP O Does not exists

A particle is moving in xy plane. Its motion is described by the lagrangian L mx y ox oy a xyyx x y Equation of motion in polar coordinates (1,8) is O mr Pe 2mr 0 Orora mrmwr. P mr. mrmor (P ) 0 mr where a and are constants

Consider a dynamical system of equations, Pxx5 x p 1 The phase space trajectory in px plane should be O circle O ellipse O cycloid O catinary

The potential energy function between two atoms in a diatomic molecule is defined for x0 and given by U(x)Uo a 12 X where, U, and a are positive constants. Which of the following options is correct O x a is a point of stable equilibrium. x 2a is a point of stable equilibrium. O x a is a point of unstable equilibrium x 2a is a point of unstable

In a system with two degrees of freedom, if (p, q) are the canonical coordinates, then which of the following transformations to (P, Q) is not canonical 1 (pq), Q tan2 P P 2qea sin p, Q2q e cos p (a is a constant) O Q tan p, P log (sin q) O Qp, P 9

A particle of mass m moves in three dimensions under a central potential V(r). Let Lagrangian in spherical polar coordinates is given by L m(r r8 r sin 0) V(r) Consider a quantity h defined by h mr sin0. Then which of the following is correct (In the following, t is time) Ohot O hot Ohoc t Oh is a constant of motion

Lagrangian of a particle is 1 L mxbxx. If at t0, x0, x Vo 2 mx. then the distance covered at 1 Vo is 01 02 012 04

The Poisson bracket of a p 26pq with the Hamiltonian H ap bq (where a, , a, b, are all constants) is 4a (ap bq)4pq Ba 48 (apbq)4pqab 48 (apbq)4pqab O O 4a (ap bq)4pqa

A particle moves under the influence of a potential V(x,y)2(2xy), a is a positive constant. Which of the following is correct OPx my, P, mx, 2px p, constant OPx my, P, mx, px 2p, constant O Px my, p, mx, 2px p, constant,Op mx, p my, p, 2p constant

The time evolution of a 1D dynamical system is described by, Yn1 y2y 2 O y 2 is a stable fixed point Oy 2 is an unstable fixed point Oy 3 is a stable fixed point O y 3 is an unstable fixed point

Lagrangian of a system is L1 a is 2x If quantity axxB It is conserved then value of,01 01 12

11 2 0 2gy O y 3,Consider lagrangian of a system of particles to be Lm3x xy 2ymg (3xy) If system starts from rest then x is always equal to

Ocg3 None of these,A particle of mass m is thrown upward under gravity. Its position is explicitly dependent on time as y(t)abtct with boundary condition at y0, at t0 r, Action between t 0 and f minimum is under the condition Obg3 Obg5

Consider a particle governed by a lagrangian in xy plane.,L m ( x y ) k (x y) This lagrangian is invariant under which of the following change of coordinates to the first order of Oxx ey y y ex O xx E y ye Oxx ey y yex None of these

The Lagrangian of a system is, L m ( x y ) x (x y) The conserved momentum is given by Om(xyjx) m (x y) m(xyxy) O mx and my

The spherical pendulum is a particle of mass m attached to a fixed point by a light inextensible string of length a and moving under uniform gravity. Its Lagrangian in polar angles 8, is given by Lma (0 sin 06) mga cos If p, and p, are conjugate momenta corresponding to and respectively, then Hamiltonian is O O 1 2ma 1 ma 1 2ma 2ma P Pe Po sin

Consider the following canonical transformation for a system with one degree of freedom QQ(q, p) q cos a p sin a P P(q, p) q sin a p cos a Here a is the angle by which Q and Pis rotated in phase space from q and p. The generating function of this transformation is given by O Og 1 2 cot a Q9 cot a (9 9) sin sin 1 (q 0) sin a Qq sin a 1 7 (q

Consider any two continuous functions of the generalised coordinates and momenta g(9k Pk) and h(qk, Pk). The poisson bracket is defined by,og ch og ch g, hk Pk Pk k pk qk Which of the following expressions is incorrect (in the following H is the Hamiltonian) 8, H g at Oq9.H. P.p,.H OP, Ps 0, 9,9, 0 O 9 P dg dt

Consider a onedimensional system with the Hamiltonian 1 H1 ( Pq) 2 The set of canonical transformation (P, Q) that reduces H to the form of a harmonic oscillator, is 1 Q , P pq 9 1, p pq P 9 2 Q, 9 P pq 0, Ppq 9

Consider two planets A and B of equal mass orbiting Sun. The time taken by both planets to go from their L1 respective perihilion to epihilion is same. The ratio of their angular momentum is, A LB 2.IfC and C denote the product of minimum (r) and maximum (r) distances of A and B from centre respectively, then OC CB OC4CB O CA CB AL 4 OC 2CB

A particle B of mass 3m is hung from a pivot O through a string of length I. If a particle A of mass m collides headon elastically with it, then the minimum value of u so that B completes a circular revolution about O is equal to m U A O5gl 25gl gl 2gl 1 B 3m

At t0 a particle has speed v. If it is acted upon by a forceby and it stops after a distances then distance covered by the particle in time is (m is mass of the particle) 0920 m In, O O

A uniform solid cylinder of mass m and radius R rolls without sliding down an inclined plane of height h. The rotational kinetic energy of the cylinder when it reaches the bottom of the plane will be mgh,Omgh2 Omgh3 mgh4

k A particle moves in a circular orbit under the action of force f (r). Ifk is suddenly reduced to half its original value, then the particle moves along Oan ellipse a parabola. O a hyperbola a circle

A planet moving around Sun in an elliptic orbit has a minimum to maximum speed ratio of 13. If max and Imin represent maximum and minimum distance of the planet from the Sun, respectively, then the max ratio is min 91 021 013 31