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Physics Questions and Answers September 26, 2022

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Consider the 2dimensional harmonic oscillator with Hamiltonian 1 P 2m mw (x y) H i) Find the energy eigenstates and eigenvalues of this Hamiltonian. Verify that the ground state is unique, while at the first excited level there are two degenerate states (Hint you do not need to do any long computation here, you just need to use the results

A 3m long ladder weighing 20 kg leans on a frictionless wall. Its feet rest on the floor 1 m from the wall as shown in Fig. Find the reaction forces of the wall and the floor. (a) N 34.6 N, N 196 N (b) N 196 N, N 34.6 N (c) N 56.4 N, N98 N (d) N 98 N, N 56.4 N 2

Three bodies, a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity (a) Sphere (b) Ring (c) Cylinder (d) All have same velocity

If the NewtonRaphson method is used to find the positive root of the qn xo 2 singe, the iteration en is 22 (sinn (n) 121052 2 (sinanIn (osam) 12005 Xntt PLAF 2 1 ( (osan In Sin n) In 2 Sin 4

Which among the curves shown in Figure cannot possibly represent electrostatic field lines,(a) (b) Conductor,(c),(d) (e)

A conductor A with a cavity as shown in Figure (a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor. (b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q q Figure (b). (c) A sensitive instrument is

Consider the hydrogen atom, and assume that the proton, instead of being a point source of the Coulomb field, is uniformly charged sphere of radius R ( ao), so that the Coulomb potential is now modified to V(r) 3e 20 (R 11) r R Calculate the energy shift for n 1, 1 0 state, and for the n 2 states, cause by this modification using the wave

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is , where is the unit vector in the outward 20 0 normal direction and o is the surface charge density near the hole.

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density without using Gausss law. Hint Use Coulombs law directly and evaluate the necessary integral.

It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called up quark (denoted by u) of charge (23) e, and the down quark (denoted by d) of charge (13) e, together

Consider the Tsection shown below. Calculate the centroid and the moment of inertia about the xx centroidal axis. The thickness of the web and the flange are the same. All angles are sharp. w40mm t10mm d80mm. X 4 W T X

Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. (b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Check that the ratio keG mm, is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify

Explain the meaning of the statement electric charge of a body is quantized. (b) Why can one ignore quantization of electric charge when dealing with macroscopic i.e., large scale charges

When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge.

Four point charges q 2 C, q 5 C, qc 2 C, and q 5 C are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 C placed at the centre of the square

An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not (b) Explain why two field lines never cross each other at any point

Two point charges qa vacuum. 3 C and q 3 C are located 20 cm apart in (a) What is the electric field at the midpoint O of the line AB joining the two charges (b) If a negative test charge of magnitude 1.5 10 C is placed at this point, what is the force experienced by the test charge

A system has two charges qa 2.5 107 C and q 2.5 107 C located at points A (0, 0, 15 cm) and B (0, 0, 15 cm), respectively. What are the total charge and electric dipole moment of the system

An electric dipole with dipole moment 4 10 C m is aligned at 30 with the direction of a uniform electric field of magnitude 5 104 N C. Calculate the magnitude of the torque acting on the dipole.

A polythene piece rubbed with wool is found to have a negative charge of 3 x 107 C. Estimate the number of electrons transferred (from which to which) (b) Is there a transfer of mass from wool to polythene

Two insulated charged copper spheres A and B have their centers separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 107 C The radii of A and B are negligible compared to the distance of separation. (b) What is the force of repulsion if each sphere is charged double the above amount,

Suppose the spheres A and B in Exercise 1.12 have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between A and B

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio

Which one of the following functions has a discontinuity in the second derivative at x 0, where x is a real variable (a) f(x) x (b) f(x)xx (c) f(x) cos(x) (d) f(x)x

Given that E, 10a, 6a, 12a, Vm in Figure (1), find (a) P, (b) E, and the angle E makes with the yaxis, (c) the energy density in each region. Figure (1) Emde

A collimated beam of laser light of wavelength 514 nm is normally incident on a smooth glass slab placed in air. Given the refractive indices of glass and air are 1.47 and 1.0, respectively, the percentage of light intensity reflected back is (a) 0 (b) 4.0 (c) 3.6 (d) 4.2

For a system undergoing a first order phase transition at a temperature T, which one of the following graphs best describes the variation of entropy (S) as a function of temperature (T) (a) S T T S S (b) (c) (d) k k k T T T T T T

The figure below shows a cubic unit cell with lattice constant a . The shaded crystallographic plane intersects the xaxis at 0.5 a. The Miller indices of the shaded plane are (a) (210) (b) (210) (c) (110) (d) (102) y

Three point charges each carrying a charge q are placed on the vertices of an equilateral triangle of side L. The electrostatic potential energy of the configuration is 1 g 1 g L 2 q L 3 q L L (a) (b) (c) (d)

Which of the following statements is correct Given n m(nm) (a) cos ne cos ( (b) sin no n ( n (2) cos n1 Cos (c) cos ne cos 0 (d) sin necos 0. is the binomial coefficient n 2 (1) 2 n2 n Osin 0 COS 3 Osin 0 n3 cos2 Osin 0 cos Osin 0 n2 n 4) Cos 0 sin 0... n 4 cos40sin 0... n 4 cos n4 0 sin 0.... COS esin 0....

Prove that the energy levels of a quantum mechanical harmonic oscillator are quantized.

Two objects of masses m and 2m are moving at speeds of v and v2, respectively. After undergoing a completely inelastic collision, they move together with a speed of v3. The angle between the initial velocity of the two objects is (a) 60 (b) 120 (c) 45 (d) 90

A short rod of length L and negligible diameter lies along the optical axis of concave mirror at a distance of 3 m. The focal length of the mirror is 1m and L 1m. If I is the length of image of the object in the mirror, then L L (a) 4 (b) L L (c) L 1 L 16 (d) L 1 4 L

Consider an annular region in free space containing a uniform magnetic field in the z direction, schematically represented by the shaded region in the figure. A particle having charge Q and mass M starts off from point P(a,0,0) in the x direction with constant speed v. If the radii of inner and outer circles are a and b, respectively, the minimum

A thin conducting square loop of side L is placed in the first quadrant of the xyplane with one of the vertices at the origin. If a changing magnetic field B(t)B (5zyt xzxty3yt 2) is applied, where Bo is a constant, then the magnitude of the induced electromotive force in the loop is (a) 4B L (b) 3B L (c) 2B, L (d) B.L

A point charge 10 C is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square (Hint Think of the square as one face of a cube with edge 10 cm.) 10 cm. 5 cm 10 cm

Prove that the torque required to keep an object in uniform circular motion is given by T = mv^2/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.

Prove that the total energy of a satellite in orbit around the Earth is given by E = -GMm/2a, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and a is the semi-major axis of the orbit.

Prove that the frequency of a photon emitted by an atom in a transition between two energy levels is given by the Rydberg formula: f = R*(1/(nf^2) - 1/(ni^2)) where R is the Rydberg constant, nf and ni are the final and initial energy levels, respectively.

A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 10 NC and points radially inward, what is the net charge on the sphere

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 x 1022 Cm. What is E (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates

A cylinder with a radius of 0.5m and a height of 2m is filled with a liquid of density 800 kg/m^3. What is the weight of the liquid in the cylinder?

A person uses 500 joules to load a couch into a truck. This task takes him 5 minutes to accomplish. How much power did he use to complete this task in this amount of time?

An object is thrown vertically upward with an initial velocity of 20 m/s. How long will it take for the object to reach its highest point and what will be the maximum height reached by the object?

A car with a mass of 1000 kg is traveling at a constant velocity of 20 m/s. The driver applies the brakes, causing the car to come to a stop in a distance of 100 meters. What is the braking force that was applied?

A projectile is launched at a velocity of 40 m/s at an angle of 60 degrees to the horizontal. What is the maximum height reached by the projectile and how long will it take for the projectile to reach that height?

A block of mass 2 kg is placed on an inclined plane with an angle of 30 degrees to the horizontal. The coefficient of friction between the block and the plane is 0.3. What is the minimum force required to prevent the block from sliding down the plane?

A car is driving at a constant speed of 20 m/s and the driver applies the brakes, causing the car to come to a stop in 8 seconds. Using the equations of motion, calculate the acceleration of the car and the distance the car travels before stopping.

A ball is thrown horizontally from the top of a building that is 15 m tall. Using the equations of motion, calculate the horizontal distance the ball will travel before hitting the ground, and the time it will take to reach the ground.

A 0.2 kg object is thrown upward with an initial velocity of 10 m/s. Using the equations of motion, calculate the maximum height the object will reach and the time it will take to reach that height.

A car is traveling at a velocity of 40 m/s and then brakes to come to a stop. Using the equations of motion for constant acceleration, calculate the distance traveled by the car and the time taken to stop, assuming a constant deceleration of -8 m/s^2. Show all calculations and include the value of the initial velocity and deceleration in your

A roller coaster train is traveling at a velocity of 20 m/s at the top of a hill that is 25 meters high. Using the principles of conservation of energy and the equation for potential energy, calculate the speed of the train at the bottom of the hill, assuming no energy is lost due to friction or air resistance. Show all calculations and include

The release of energy in nuclear fission is consistent with the fact that uranium has more mass per nucleon than the two fragments. more kinetic energy than the two fragments. exactly the same mass per nucleon as the two fragments. less mass per nucleon than the two fragments.

A spaceship is traveling at a velocity of 0.8c (where c is the speed of light) and is approaching a planet that has a mass of 2 x 10^29 kg. Using the principles of special relativity, calculate the relativistic mass of the spaceship as it approaches the planet, and the gravitational force acting on the spaceship as it comes within 100,000 km of

A ball is thrown upwards with an initial velocity of 30 m/s from the top of a building that is 50 meters tall. Using the equations of motion for constant acceleration, calculate the time it takes for the ball to reach its maximum height, and the maximum height it reaches. Show all calculations and include the value of the acceleration due to

a) Starting with Ficks Law of diffusion, derive the following equation for gas phase molar flux of material A diffusing through a stagnant layer of gaseous material B NA Po DA total AB RT Z21 PAIPA2 PBM A1 b) Show how the diffusivity DAB may be calculated if a dense sphere of a volatile solid A is suspended in a layer of static gas B.

Refer to the schematic (image). It has a power supply Vcc, a resistor R, and a LED. Assume that Vcc 6.0 volts. Assume that the LED is a Kingbright Green LED. Refer to the Appendix for the Kingbright LED datasheet and answer the questions below. The target current that the circuit should allow is 5 mA. What is the voltage drop across the LED under

Consider a measure space (0, 2pai, ML 0, 2pai, ,meuL). Define a signed measure of ta on this space by setting X(E) sin rd, for EM, 0, 2. E Let C . Let e 0 be arbitrary given. Find a measurable set CCC such that X(C) X(C) and X(E) for every measurable subset E of C.

refer to a thin, nonconducting ring of radius R, as shown below, which has a charge Q uniformly spread out on it. photobucket The electric potential at a point P, which is located on the axis of symmetry a distance x from the center of the ring, is given by A. Q(4.78X) B. Q470 (Rx) 2 C. Qx4.7E (Rx) D. Qx47E (Rx)32 E. QR4.7 (Rx),Question 34 refer

The capacitor shown in Figure 1 above is charged by connecting switch S to contact a. If switch S is thrown to contact b at time t 0, which of the curve in Figure 2 above represents the magnitude of the current through the resistor R as a function of time

The resistance of a strip of copper of rectangular crosssection is 202. A metal of resistivity twice that of copper is coated on its upper surface to a thickness equal to that of copper strip. The resistance of composite strip will be (a) 6 (b) 430 (c) 320 (d) 340

For the system shown in figure, with a damping ratio of 0.7 and an undamped natural frequency wn of 4 rad sec, the values of K and are (a) K 4, a 0.35 (b) K 8, a 0.455 (c) K 16, a 0.225 (d) K 64, 0.9 aquery 5(52) 1as R(S) ((s)

If the secondary winding of the ideal transformer shown in the figure below, has 40 turns, the number of turns in the primary winding for maximum power transfer to the 2 ohm resistor will be IDEA TRANSFORMER (a) 20 (b) 40 8.n. elle (c) 80 eller 40 TURNS (d) 160

A 6 pole 3phase woundrotor induction machine is driven by another machine at 1800 rpm. The rotor of the induction machine is connected to a 50Hz system. If the mechanical rotation of the rotor is in the same direction as the rotor winding flux rotation, then frequency of the stator voltage will be (a) 50Hz (b) 140 Hz (c) 150 Hz (d) 200 Hz

Two 550 kVA alternator operate in parallel to supply the following loads I. 250 KW at 0.95 p.f. lagging II. 100 KW at 0.85 p.f. leading One machine is supplying 200 KW at 0.9 p.f. lagging. The p.f. of other machine must be (a) 0.89 leading (b) 0.95 leading (c) 0.95 lagging (d) 0.89 lagging

In a 110 volts compound generator, the armature, shunt and series windings are 0.06 ohm, 27.5 ohm and 0.04 ohm respectively. The load consists of 200 lamps each rated at 55 W, 110 V. find the total e.m.f. when the machine is connected for long shunt operation. (a) 12 V (b) 72 V (c) 100 V (d) 120 V

The copper armature winding of a motor is subjected to an operating temperature of 80C. The room temperature is 20 C. The percentage change in resistance of the armature winding from cold staring condition to normal running will be nearly (a) 10 (b) 16 (c) 20 (d) 24

Two resistance 1000 50 150 are connected in series. If the errors are specified as standard deviations, the resultant error will be (a) 100 (b) 10.60 (c) 15.80 (d) 200

The unit impulse response of a system is given as c (t) 4et 6e2. The step response of the same system for 20 is equal to (a) 3et 4e 1 (b) 3et 4e1 (c) 3e2t 4et1 (d) 3e2t 4et1

An undesirable side effect of motional inductance of large conduction specimens is (a) Skin effect (b) hysteresis (c) eddy currents (c) dielectric loss

A load that has a resistance of 10 ohms is to be connected to a supply that has a constant voltage of 120 volts. If it is desired that the current to the load be varied from 3 to 5 amperes, what are the resistance and the current rating of the series rheostat that permit this variation (a) (a) 5 ohms, 5 A (b) (c) 20 ohms, 10 A (b) 10 ohms, 10 A

All of the following comparisons between metals and metal alloys and ceramics are true except (a) ceramic compounds crystallize more slowly then metallic compounds (b) ceramic compounds have higher melting temperatures than metallic compounds (c) Metallic compounds are better conductors or current than ceramic compounds at higher temperatures. (d)

A centre zero ammeters connected in the rotor circuit of a 6pole 50 Hz induction motor makes 30 oscillations in one minute. The rotor speed is (a) 970 (b) 990 (c) 1010 (d) 1030

A 220 V dc machine has an armature resistance of 1ohm. If the full load current is 20A, the difference in the induced voltage when the machine is running as a motor, and as a generator is (a) 20 V (b) zero (c) 40 V (do 50 v

The function ecosx is Taylor expanded about x 0. The coefficient of x is

The 80kg man can throw the 20kg box horizontally at 4 ms when standing on the ground. If instead he firmly stands in the 120kg boat and throws the box, as shown in the photo, determine how far the boat will move in three seconds. Neglect water resistance.

For the given circuit, VD is the threshold voltage of the diode. The graph that best deposits variation of Vo, with Vi is

A solid cone hangs from the frictionless pivot at the origin O as shown above.

Arrange the following telescopes, where D is the telescope diameter and pai is the wavelength, in order of decreasing resolving power I. D 100m, 21cm II. D 2m, 500 nm III. D1m, 100 nm (a) III, II, IV, I (c) IV, III, II, I IV. D2m, 2 10mm (b) II, III, I, IV (d) III, II, I, IV

A. A cylindrical tube of mass M can slide on a horizontal wire. Two identical pendulum, each of mass m and length 1, hang from the ends of the tube, as shown above. For small oscillations of the pendulums in the plane of the paper, the eigenfrequencies of the normal modes of oscillation of the system g(M2m), and... IM are o.. B. C. gM m VT M D.

The moment of inertia of a solid sphere (radius R and mass M) about the axis which is radius R and mass M 2 at a distance of (a) 3 MR 20 M from the centre is (b) MR (c) 13 20 MR (4) M 10 MR

Three events, E (ct0, x0), E (ct0, xL) and E (ct0, xL) occur, as observed in an inertial frame S. Frame S is moving with a speed v along the positive x direction with respect to S. In S, let t,,t be the respective times at which E, E and E, occurred. Then, (a) t

The solution y(x) of the differential equation y dydx3x 0, y(1)0, is described by (a) an ellipse (b) a circle (c) a parabola (d) a straight line

A particle initially at the origin in an inertial frame S, has a constant velocity Vi. Frame S is rotating about the zaxis with angular velocity (anticlockwise). The coordinate axes of S coincide with those of S at t0. The velocity of the particle (V,V) in the 200 S frame, at t () () is (b) (V,V) (c) (d) 3V

For the given circuit, the output y is (a) 0 (b) 1 (c) A Y (d) A

The total charge contained within the cube (see figure), in which the electric field is given by E K (4xi3y), where is the permittivity of free space, is (a) 7Ks (001) (b) 5K (010) (000) (100) (c) 33K X (d) Zero

Four charges are placed very closed to each other, as shown. The separation between the two charges on the yaxis is a. The separation between the two charges on the x axis is also a. The leading order (nonvanishing) form of the electrostatic potential, at point P, at a distance from the origin (ra), is P (a) (c) 1qa (31) 2002 qa (51) a 9 q 0 60

A mass m is connected to a massless spring of spring constant k, which is fixed to a wall. Another mass 2m, having kinetic energy E, collides collinearly with the mass m completely inelastically (see figure). The entire set up is placed on a frictionless floor. The maximum compression of the spring is (a) 4E 3k (b) E 3k m (c) 2m E 5k (d) E 7k

In the Fourier series expansion of two functions f(t)4t 3 and f (t) 6t 7t in the interval T2 to T2 the Fourier coefficient a, and b (a, and b, are coefficients T T 2 2 of cos (not) and sin (not), respectively) satisfy (a) a 0 and b 0 for f(t) a, 0 17 (b) a, 0 and b 0 for f(t) a, 0 (c) a, 0 and b, 0 for f(t) a, 0 (d) a, 0 and b, 0 for fi (t)

A gaseous system, enclosed in an adiabatic container, is in equilibrium at pressure P, and volume V. Work is done on the system in a quasistatic manner due to which the pressure and volume change to P and V, respectively, in the final equilibrium state. At Cp Cv every instant, the pressure and volume obey the condition PV C, where y and C is a

An isolated ideal gas is kept at pressure P and volume V. The gas undergoes free expansion and attains a pressure P and volume V. Identify the correct statements(s) (1) (a) This is an adiabatic process (c) PV PV (b) PV PV (d) This is an isobaric process

A beam of light travelling horizontally consists of an unpolarized component with intensity I, and a polarized component with intensity I. The plane of polarization is oriented at an angle with respect to the vertical. The figure shows the total intensity Ilotal after the light passes through a polarizer as a function of the angle a, that the axis

Consider the following differential equation that describes the oscillations of a physical system dy a B. dt dy yy0 dt If a and are held fixed, and y is increased, then, (a) The frequency of oscillations increases (b) The oscillations decay faster (c) The frequency of oscillations decreases (d) The oscillations decay slower

A parallel plate capacitor having plate area of 50 cm and separation of 0.1 mm is completely filled with a dielectric (dielectric constant K 10). The capacitor is connected to a 10k resistance and an alternating voltage v 10 sin (100 zt), as shown in the figure. The switch S is initially open and then closed at t0. The ratio of the displacement

A thin film of alcohol is spread over a surface. When light from a tunable source is incident normally, the intensity of reflected light at the detector is maximum for 640nm and minimum for 512 nm. Taking the refractive index of alcohol to be 1.36 for both the given wavelengths, the minimum thickness of the film would be nm (Round off to two

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q. The probability that any point picked randomly within the square falls in the shaded area is (a) 4 T 2 (b) (c) 21 (d)

Choose the graph that best describes the variation of dielectric constant (,) with temperature (7) in ferroelectric material. (Te is the Curie temperature) (a) (c) Te Tc Er T T (b) (d) , M Te Te T T

Consider a crosssection of an electromagnet having an airgap of 5 cm as shown in the figure. It consists of a magnetic material ( 20000,) and is driven by a coil having NI 10 A, where N is the number of turns and I is the current in Ampere. 20000 3cm 3cm Air gap 3cm 3cm 3 cm 9 cm 17 cm 5cm Ignoring the fringe fields, the magnitude of the

Consider an atomic gas with number density n1020 m, in the ground state at 300 K. The valence electronic configuration of atoms is f. The paramagnetic susceptibility of the gas xmx10. The value of m (rounded off to two decimal places) is (Given Magnetic permeability of free space 47x10Hm Bohr magneton 9.274x1024 Am Boltzmann constant k