Physics Questions and Answers October 23, 2022

Design a subtractor using operational amplifier in difference amplifier mode.

If electric field intensity at a certain distance from a dipole on its axis is El and at the same distance but on the perpendicular bisector of the dipole is E2, then a) E1E2 b) E12 E2 c) El4 E2 d) E13 E2

What are band pass filters? On what basis are wide band pass and narrow band pass filters distinguished? Draw their typical frequency response. Draw circuit diagram of a wide band pass filter.

Explain the functioning of a logarithmic amplifier.

An electric dipole is placed inside a cube. What will be the nature of electric flux from the cube surface a) Coming out of the surface b) Coming in towards the surface c) No flux at all d) Coming out from one half and coming inwards in another half

What is an all-pass filter? Derive the expression for its voltage gain and phase difference.

Design a first-order low-pass filter at a cut off frequency of 4KHz and pass-band gain of 4. Draw its frequency response.

If an electric dipole is placed in a uniform electric field dipole. a) A force but no torque b) Both force and torque c) Torque but no force d) No torque or force will act on the

A circular annulus of inner radius r and outer radius R has a uniform charge density a. What will be the total charge on the annulus a) a(Rr) b) a(Rr) c) a (Rr) d) a R

Electric field outside this Gaussian surface will be . q2 .91 q1 a) Only for q2 b) Only for positive charges c) Zero d) For all the charges

Let S stand for the set of all natural numbers that are perfect squares, so S 1,4,9,16,25,36,49,64,...). Show that the set S and the set of all natural numbers have the same cardinality by describing an explicit onetoone correspondence between the two sets. (b) Take the set of natural numbers and remove a first 7 numbers from it. Then, show that

8 electric dipoles having charges e are placed at the center of a cube. The net flux coming out of the cube surface is a) Zero b) eo c) 8eo d) 16eo

The solution of the differential equation x y ex with the boundary condition y (x 1) 0, misd (A) (x 1) X (C) (1x) ex dy (1x) dx ex (B) (x) (D) (x 1) ex ex xd 3

The value of the definite integral S is (A) 43 (C) de 54 cos 0 (B) 23 tod (D) 3161 3 nuong

Two coherent plane electromagnetic waves of wavelength 0.5 m (both have the same amplitude and are linearly polarized along the zdirection) fall on the y 0 plane. Their wave vectors k and k are as shown in the figure Innston Chungo ni gnivom sloins A (0) k ( norkutovaw.syd zi (1) bus og do 101 q adatto 101 noitizog sdi ugas Istot odi (5(x) 1019

The elements of a 3 x 3 matrix A are the products of its row and column indices A. ij (where i, j 1,2,3). The eigenvalues of A are (A) (7,7,0) (B) (7,4, 3) (C) (D) (14,0,0) 14 14 14 333 (0)

An npntransistor is connected in a voltage divider as shown in the figure below 20 V R 80 kq R 20 ks W B Rc 5 kQ2 c E www. B 50 R 1 kQ rd If the resistor R is disconnected, the voltages VB at the base and Vc at the collector change as follows 2107 (A) Both VB and Vc increase (B) Both VB and Vc decrease (C) VB decreases, but Vc increases C (D)

A particle of mass mo and charge e oscillates along the xaxis in a 1D Harmonic potential with an angular frequency w. It an electric field e is applied along the xaxis, evaluate the first and second order corrections to the energy of the 4th State.

A onedimensional box of length a contains two particles each of mass m. the interection bw the particles is described by a potential of the type VL4, x) 1 (xx). Calculate the ground. State energy to first order qud.

Consider an atomic State specified by auguler momenta 1, and 3 1 5 placed in a magnetic field is. Treating the Futeraction representing the maquetic moment of the electron qu the magnetic field as the perturbing Hamiltonian and writing 23 9, obtain an expression for (i) the gfactor of the 7th state is the corrected energy.

A simple pendulam of length I swings in a vertical plane under the influence of gravity. In the smell angle approximation, find the energy levels of the system. Also evaluate the first order correction to the ground state energy taking one more term in the small angle approximation.

The Hamiltonian matrix of a system in the orthonormal basis 1 0 0 ,0 1 0,0 0 1 is given by H 1 2e 0,2e 2e 3e, 0 3e 3e. Find the energy levels. corrected up to second order fu the small parameter E.

Charges 50 x 10C, 25 x 10 C and 10 10 C are held fixed at the three corners A, B, C of an equilateral triangle of side 50 cm. Find the electric force on the charge at C due to the rest two.

Two particles A and B having charges 80 x 10C and 20 10C respectively are held fixed with a separation of 20 cm. Where should a third charged particle be placed so that it does not experience a net electric force

Three equal charges, each having a magnitude of 20 10 C, are placed at the three corners of a right angled triangle of sides 3 cm, 4 cm and 5 cm. Find the force on the charge at the rightangle corner.

Two small iron particles, each of mass 280 mg, are placed at a distance 10 cm apart. If 0.01 of the electrons of one particle are transferred to the other, find the electric force between them. Atomic weight of iron is 56 g mol and there are 26 electrons in each atom of iron.

A charge Q is to be divided on two objects. What should be the values of the charges on the objects so that the force between the objects can be maximum

Two particles, each having a mass of 5 g and charge 10x 10 C, stay in limiting equilibrium on a horizontal table with a separation of 10 cm between them. The coefficient of friction between each particle and the table is the same. Find the value of this coefficient.

Three charges, each equal to q, are placed at the three corners of a square of side a. Find the electric field at the fourth corner.

A charged particle of mass 10 g is suspended through a silk thread of length 40 cm in a horizontal electric field of 40 x 10NC. If the particle stays at a distance of 24 cm from the wall in equilibrium, find the charge on the particle.

A particle A having a charge of 50 x 10 C is fixed in a vertical wall. A second particle B of mass 100 g and having equal charge is suspended by a silk thread of length 30 cm from the wall. The point of suspension is 30 cm above the particle A. Find the angle of the thread with the vertical when it stays in equilibrium.

Four particles, each having a charge q, are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon.

Find the electric field at a point P on the perpendicular bisector of a uniformly charged rod. The length of the rod is L, the charge on it is Q and the distance of P from the centre of the rod is a.

A uniform electric field E is created between two parallel, charged plates as shown in figure (29W9). An electron enters the field symmetrically between the plates with a speed v.. The length of each plate is I. Find the angle of deviation of the path of the electron as it comes out of the field. Vo E

Charges 20 x 10C and 10x10C are placed at corners A and B of a square of side 50 cm as shown in figure (29W10). How much work will be done against the electric field in moving a charge of 10 x 10 C from C to D D A 5 cm C B

Three point charges q, 2q and 8q are to be placed on a 9 cm long straight line. Find the positions where the charges should be placed such that the potential energy of this system is minimum. In this situation, what is the electric field at the charge q due to the other two charges

Shows an electric dipole formed by two particles fixed at the ends of a light rod of length 1. The mass of each particle is m and the charges are q and q. The system is placed in such a way that the dipole axis is parallel to a uniform electric field E that exists in the region. The dipole is slightly rotated about its centre and released. Show

A uniform electric field of magnitude E 100 N C exists in the space in xdirection. Calculate the flux of this field through a plane square area of edge 10 cm placed in the yz plane. Take the normal along the positive xaxis to be positive.

A large plane charge sheet having surface charge density o20 x 106 Cm lies in the xy plane. Find the flux of the electric field through a circular area of radius 1 cm lying completely in the region where x, y, z are all positive and with its normal making an angle of 60 with the zaxis.

An electric dipole consists of charges 20x10C separated by a distance of 20 x 10 m. It is placed near a long line charge of linear charge density 40 x 10 Cm as shown in figure (30W4), such that the negative charge is at a distance of 20 cm from the line charge. Find the force acting on the dipole. 1 2.0 cm

A particle of mass 5x10 g is kept over a large horizontal sheet of charge of density 40 x 10C m2 (figure 30W5). What charge should be given to this particle so that if released, it does not fall down How many electrons are to be removed to give this charge How much mass is decreased due to the removal of these electrons

Two conducting plates A and B are placed parallel to each other. A is given a charge Q, and B a charge Q Find the distribution of charges on the four surfaces.

A parallelplate capacitor has plates of area 200 cm and separation between the plates 100 mm. What potential difference will be developed if a charge of 1.00 nC (i.e., 100 x 10 C) is given to the capacitor If the plate separation is now increased to 200 mm, what will be the new potential difference 9

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Consider the connections shown in figure (31W1). (a) Find the capacitance between the points A and B. (b) Find the charges on the three capacitors. (c) Taking the potential at the point B to be zero, find the potential at the point D. 6 F 12 F D 2 F 4 24 V B

De If 100 volts of potential difference is applied between a and b in the circuit of figure (31W2a), find the potential difference between c and d. 6 F 6 F (a) HH 6 F 6 F d b 100 V HH 2 Q (b) Q2 Q C 3 Q 0 414 d

Find the charges on the three capacitors shown in figure (31W3a). 2 F 6V (a) 4 F 5F 6 V 2 F 6V 00 1 V 5F 6V (QQ) T9 9) 0 4 F Q2 Q2 6V (b) 6 V

Twelve capacitors, each having a capacitance C, are connected to form a cube (figure 31W6a). Find the equivalent capacitance between the diagonally opposite corners such as A and B. (a) B 4 Q3 (b) E Q6 9 Q3 8

The negative plate of a parallel plate capacitor is given a charge of 20 x 10 C. Find the charges appearing on the four surfaces of the capacitor plates.

The connections shown in figure (31W9a) are established with the switch S open. How much charge will flow through the switch if it is closed 24 V H 1 F 2 F (a) S 2F 1 F 24 V To tollig 1 F 2 F H QQ (b) 4 S Vo Q29 2 2 F 1 F HH Q 3

Each of the three plates shown in figure (31W10a) has an area of 200 cm on one side and the gap between the adjacent plates is 0.2 mm. The emf of the battery is 20 V. Find the distribution of charge on various surfaces of the plates. What is the equivalent capacitance of the system between the terminal points A B (a) C A Q2 Q2 B (b) 20 V Q2 Q2 (3 C

Find the capacitance of the infinite ladder shown in figure (31W11). A. B 91 91 C Q 91 Figure 31W11 C

A parallelplate capacitor is formed by two plates, each of area 100 cm, separated by a distance of 1 mm. A dielectric of dielectric constant 50 and dielectric strength 19 x 10 Vm is filled between the plates. Find the maximum charge that can be stored on the capacitor without causing any dielectric breakdown.

The space between the plates of a parallelplate capacitor of capacitance C is filled with three dielectric slabs of identical size as shown in figure (31W13). If the dielectric constants of the three slabs are K, K and Ka, find the new capacitance. A K K B K3

A parallelplate capacitor of capacitance 100 F is connected to a power supply of 200 V. A dielectric slab of dielectric constant 5 is now inserted into the gap between the plates. (a) Find the extra charge flown through the power supply and the work done by the supply. (b) Find the change in the electrostatic energy of the electric field in the

A parallelplate capacitor is placed in such a way that its plates are horizontal and the lower plate is dipped into a liquid of dielectric constant K and density p. Each plate has an area A. The plates are now connected to a battery which supplies a positive charge of magnitude Q to the upper plate. Find the rise in the level of the liquid in the

An electron moves in a circle of radius 10 cm with a constant speed of 40 x 10 ms. Find the electric current at a point on the circle.

A current of 2.0 A exists in a wire of cross sectional area 10 mm. If each cubic metre of the wire contains 28 60 x 10 free electrons, find the drift speed.

Find the resistance of a copper coil of total wirelength 10 m and area of cross section 10 mm. What would be the resistance of a similar coil of aluminium The resistivity of copper 1.7 x 10 Qm and that of 26 x 108 Q2 m. aluminium 8

A parallelplate capacitor has plates of area 10 cm separated by a distance of 1 mm. It is filled with the dielectric mica and connected to a battery of emf 6 volts. Find the leakage current through the capacitor. Resistivity of mica 1 x 10 m. 13

Find the resistance of a hollow cylindrical conductor of length 10 m and inner and outer radii 1.0 mm and 2.0 mm respectively. The resistivity of the material is 8 2.0 1089 m.

In the circuit shown in figure (32W13a) E, F, G and H are cells of emf 2, 1, 3 and 1V respectively. The resistances 2, 1, 3 and 19 are their respective internal resistances. Calculate (a) the potential difference between B and D and (b) the potential differences across the terminals of each of the cells G and H. 2V E G 252 202 3V 3 B 1 V 102 C

Find the currents going through the three resistors R, R and R, in the circuit of figure (32W15a). E R E R3 B (a) E2 R2 D 1 R3 1124 B (b) E2 R2 12

Find the equivalent resistance of the circuit of the previous problem between the ends of an edge such as a and b in figure (32W19a). TO P 121 1 112 (b) 2 1112 9 4112 2(11)

Find the equivalent resistance of the network shown in figure (32W21) between the points a and b. a 10 5 5 2.5 e 5 2.5 5 10

Find the current i supplied by the battery in the network shown in figure (32W23) in steady state. (b) Find the charge on the capacitor. 2V HE 2F 652 402 Figure 32W23

A part of a circuit in steady state along with the currents flowing in the branches, the values of resistances, etc., is shown in figure (32W24). Calculate the energy stored in the capacitor. 4 V 3 V 2 A 2 A 192 192 32, P 4 F Q 3 1 A 1A 5 202 Figure 32W24 S 192 4

Q Find the potential drops across the two resistors shown in figure (32W25a). (b) A voltmeter of resistance 600 is used to measure the potential drop across the 3000 resistor. What will be the measured potential drop 300 100 V (a) 200 600 300 2 Figure 32W25 100 V (b) 20002

A galvanometer has a coil of resistance 100 2 showing a fullscale deflection at 50 A. What resistance should be added to use it as (a) a voltmeter of range 50 V (b) an ammeter of range 10 mA

The electric field between the plates of a parallelplate capacitor of capacitance 20 F drops to one third of its initial value in 44 us when the plates are connected by a thin wire. Find the resistance of the wire.

A capacitor is connected to a 12 V battery through a resistance of 10 2. It is found that the potential difference across the capacitor rises to 40 V in 1 us. Find the capacitance of the capacitor.

A capacitor charged to 50 V is discharged by connecting the two plates at t 0. If the potential difference across the plates drops to 10 V at t 10 ms, what will be the potential difference at t 20 ms

A 50 F capacitor having a charge of 20 C is discharged through a wire of resistance 50 2. Find the heat dissipated in the wire between 25 to 50 s after the connections are made.

A current of 30 A is registered when the terminals of a dry cell of emf 1.5 volts are connected through an ammeter. Neglecting the meter resistance, find the amount of heat produced in the battery in 10 seconds.

A room heater is rated 500 W, 220 V. (a) Find the resistance of its coil. (b) If the supply voltage drops to 200 V, what will be the power consumed (c) If an electric bulb rated 100 W, 220 V is connected in series with this heater, what will be the power consumed by the heater and by the bulb when the supply is at 220 V

A battery of emf and internal resistance r is used in a circuit with a variable external resistance R. Find the value of R for which the power consumed in R is maximum.

A silver and a copper voltameter are connected in series with a 120 V battery of negligible resistance. It is found that 0806 g of silver is deposited in half an hour. Find (a) the mass of the copper deposited and (b) the energy supplied by the battery. ECE of silver 112 x 10 kg C and that of copper 66 x 10 kg C.

A current of 1 A is passed through a dilute solution of sulphuric acid for some time to liberate 1 g of oxygen. How much hydrogen is liberated during this period How long was the current passed Faraday constant 96500 C mol.

Two long wires a and b, carrying equal currents of 100 A, are placed parallel to each other with a separation of 400 cm between them as shown in figure (35W1). Find the magnetic field B at each of the points P, Q and R. 2.00 cm2.00 cm2.00 cm 2.00 cm2.00 cm P a Q Figure 35W1 R

The displacement of a particle of a string carrying a travelling wave is given by y (30 cm) sin 6.28(0.50x 50 t), where x is in centimetre and t in second. Find (a) the amplitude, (b) the wavelength, (c) the frequency and (d) the speed of the wave.

The equation for a wave travelling in xdirection on a string is y (30 cm) sin(3.14 cm) x (314 s )t. (a) Find the maximum velocity of a particle of the string. (b) Find the acceleration of a particle at x 6.0 cm at time t 0.11 s.

Two parallel wires P and Q placed at a separation d6 cm carry electric currents i, 5 A and i, 2 A in opposite directions as shown in figure (35W2a). Find the point on the line PQ where the resultant magnetic field is zero. P d (a) 2 Figure 35W2 (b) 2 R

A long string having a crosssectional area 0.80 mm and density 125 g cm, is subjected to a tension of 64 N along the Xaxis. One end of this string is attached to a vibrator Imoving in transverse direction at a frequency of 20 Hz. At t0, the source is at a maximum displacement y 10 cm. (a) Find the speed of the wave travelling on the string. (b)

Two long, straight wires a and b are 20 m apart, perpendicular to the plane of the paper as shown in figure (35W3). The wire a carries a current of 96 A directed into the plane of the figure. The magnetic field at the point p at a distance of 1011 m from the wire b is zero. Find (a) the magnitude and direction of the current in b, (b) the

The speed of a transverse wave, going on a wire having a length 50 cm and mass 5.0 g, is 80 m s. The area of cross section of the wire is 1.0 mm and its Young modulus is 16 10 N m 2. Find the extension of the wire over its natural length.

A current of 200 A exists in a square loop of edge 100 cm. Find the magnetic field B at the centre of the square loop.

Two waves passing through a region are represented by y (10 cm) sin(314 cm x (157 st and y (1.5 cm) sin (157 cm)x (314 s)t. Find the displacement of the particle at x 4.5 cm at time t 5.0 ms.

The vibrations of a string fixed at both ends are described by the equation y (5.00 mm) sin((157 cm) x sin(314 s) t (a) What is the maximum displacement of the particle at x 566 cm (b) What are the wavelengths and the wave speeds of the two transverse waves that combine to give the above vibration (c) What is the velocity of the particle at x

A guitar string is 90 cm long and has a fundamental frequency of 124 Hz. Where should it be pressed to produce a fundamental frequency of 186 Hz

Two long wires, carrying currents i, and i, are placed perpendicular to each other in such a way that they just avoid a contact. Find the magnetic force on a small length dl of the second wire situated at a distance l from the first wire. 1 1 dl Figure 35W5

Find the magnetic field at the point P in figure (35W8). The curved portion is a semicircle and the straight wires are long. P Figure 35W8 d

A wire having a linear mass density 5.0 10 kg m kg m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire.

One end of a wire 2 m long and 0.2 cm in cross section is fixed in a ceiling and a load of 4.8 kg is attached to the free end. Find the extension of the wire. Young modulus of steel 20 10 N m. Take g 10 m s.

The magnetic field B due to a currentcarrying circular loop of radius 12 cm at its centre is 0.50 10 T. Find the magnetic field due to this loop at a point on the axis at a distance of 50 cm from the centre.

One end of a nylon rope of length 4.5 m and diameter 6 mm is fixed to a treelimb. A monkey weighing 100 N jumps to catch the free end and stays there. Find the elongation of the rope and the corresponding change in the diameter. Young modulus of nylon 11 2 4.8 x 10 N m and Poisson ratio of nylon 0.2.

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure The breaking stress of the metal is 2 x 10N m. What should be the minimum radius of the wire used if it is not to break Take g 10 m s. 1 kg 5 2 kg

A long, straight wire carries a current i. A particle having a positive charge q and mass m, kept at a distance xo from the wire is projected towards it with a speed v. Find the minimum separation between the wire and the particle.

Two wires of equal cross section but one made of steel and the other of copper, are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. Find the ratio of the lengths of the two wires. Young modulus of steel 2.0 x 10 N m and that of copper 1.1 x 10 N m. and

3 Find the decrease in the volume of a sample of water from the following data. Initial volume 1000 cm, initial pressure 10 N m, final pressure 10 N m, compressibility of water 50 x 10 m N.

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Find the longitudinal strain in both the wires. Area of cross section of each wire is 0.005 cm and Young modulus of the metal is 20 x 10 N m. Take g 10

A 1 charge of 2.0 C moves with a speed of 20 x 10 m along the positive xaxis. A magnetic field B of strength (020j040 k)T exists in space. Find the magnetic force acting on the charge.