Physics Questions and Answers September 22, 2022

Given the signal m(t) 10 cos 2000 t cos 8000 t. What is the minimum sampling rate based on the lowpass uniform sampling theorem Repeat it based on the bandpass sampling theorem.

What is the average period of rotation of HCI molecule if it is in the J1 state. The internuclear distance of HCI is 0.1274 nm. The mass of SE H1.673 x 1027 kg and that of Cl 58.06 x 1027 kg.

An operator f describing the interaction of two spin12 particles has the form f a b o..o,, where, a and b are constants, o, and o, are Pauli matrices. The total spin angular momentum is J j j (00) h2. Show that f, J and J, can be simultaneously measured. Apply the

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 14 cm and the total height of the vessel is 13 cm. Find the capacity. (TT 227)

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a litre

A rectangular sheet of metal 44 cm long and 20 cm broad is rolled along its length into a right circular cylinder so that the cylinder has 20 cm as its height. Find the volume and curved surface are of the cylinder so formed.

In Figure, suppose the switch has been closed for a time interval sufficiently long (steady state) for the capacitor to become fully charged. R 9 k0, R 13 k0, R3 3 k0, C 11x 106F, and an ideal battery has emf 13 V. Find the steady state current in resistor R. (Your result must be in mAs and include 3 digit after the decimal point. Maximum of

.A 450 g mass in a spring mass system has a maximum speed of 0.21 ms as it vibrates with an amplitude of 4.2 cm. Find (a) the spring constant,(b) the maximum acceleration of the mass,(c) the speed when the mass is 3.0 cm from its equilibrium position.

(b) its acceleration just as it is released.,A 250 g mass is attached to the end of a spring whose spring constant is k 120 Nm. The spring stretches 5.0 cm from its equilibrium position and is released. Find (a) the speed of the mass as it passes through the equilbrium position.

A) Amplitude B) Frequency C) Period of motion D) Spring constant

A 520 g mass vibrates back and forth a spring that obeys the equation Find its x 18cos(3.7t) cm

A certain spring that obeys Hookes law stretches 42 cm when a load of 0.28 N is added to it. How much elastic potential energy is stored in the spring when it is compressed by 3.35 cm.

A particular spring streches 20 cm when a 500 g mass is hung from it. Suppose the mass is replaced by a 2.0 kg mass and the system is then vibrated horizontally on a frictionless surface by displacing the mass 40.0 cm from its equilibrium position and releasing it. Find (a) the maximum velocity of the mass,(b) its maximum acceleration, and,(c) its

An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 104 N C in Millikans oil drop experiment. The density of the 1.60 x 3 oil is 1.26 g cm . Estimate the radius of the drop. (g 9.81 m s e S 10 C).

A solar panel supplies a current into a 10 2 load when exposed to the sun under optimal conditions (i.e. the suns radiation is vertical, power density is maximal) at a location where the suns radiation intensity is 1400 Wm. The panels dimensions are provided. Use the average wavelength in the visible range of 550 nm as the wavelength of radiation.

Astronauts in space move a toolbox from its initial position 6,7,6 m to its final position 12, 12, 2 m. The two astronauts each push on the box with a constant force. Astronaut 1 exerts a force F 19,6, 20 N and astronaut 2 exerts a force F15, 7,16 N. What is the total work performed on the toolbox For each of the scenarios below indicate the

Design a fourresistor bias network for a PNP transistor to give Ic 11 mA and VEC 5 V if VRE1V, Vcc15 V and BF50. Replace your exact values with the nearest values from the resistor table and find the resulting Qpoint. VEE RB2 VB RB1 V VRE VEB 0.7 IB Vcc RE VEC Vc Rc

A 1830 kg car is traveling with a speed of 19.8 ms. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 63.1 m

A toxic radioactive substance with a density of 8 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building used 35 years ago. If the substances halflife is 20 years, what was the density of the substance when it was deposited 35 years ago

Two waves travel in the same medium at the same speed. One has a wavelength of 0.0382 m and a frequency of 9.67x106 Hz. The other has a wavelength of 0.0486 m. What is the period of the second wave

A train has a speed of 60 kmhn for the first one hour and 40 kmhn for the next half hours. Its average speed in kmhn is

The velocity of a bullet is reduced from 200 msec tp 100 msec. while travelling through a wooden block of thickness 10 cm. the retardation, assuming it to be uniform can be

A stone is shot straight upward with speed of 20 ms from a tower 200 m high. The speed with which it strikes the ground is approximately

The Van der Waals equation for 1 mole of gas is (PaV2)(Vb) RT where a and b are constants. If U is the internal energy of system of n moles of gas, then(dudv) is (a) 0 (b). a(V(nb))2 (c) a(nv) (d) a(Vm)2

An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e., 120 km/h, the stopping distance will be (a) 20 m (b) 40 m (c) 60 m (d) 80 m

A ball is released from the top of a tower of height h metre. It takes T second to reach the ground. What is the position of the ball in T/3 second? (a) (h/9)meter from the ground (b) (7h/9) meter from the ground (c) (8h/9) meter from the ground (d) (17h/18) meter from the ground

From a building, two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If v A and v B are their respective velocities on reaching the ground, then (a) v B > v A (b) v A = v B (c) v A > v B (d) their velocities depend on their masses

If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest? (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground is n times that taken by it to reach the highest point of its path. The relation between H, u and n is (a) gH = (n 2)u 2 (b) 2gH = n 2u 2 (c) gH = (n 2)2u 2 (d) 2gH = nu 2 (n 2)

A car, starting from rest, accelerates at the rate f through a distance s, then continues at a constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed in 15 s, then (a) s= ft 2 (b) s= ()ft 2 (c) s = ft (d) s= (1/72)ft 2

A parachutist after bailing out falls 50 m without friction. When the parachute opens, it decelerates at 2 m/s 2 . He reaches the ground with a speed of 3 m/s. At what height, did he bailout? (a) 293 m (b) 111 m (c) 91 m (d) 182 m

An automobile travelling at 40 km/h can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding) (a) 100 m (b) 75 m (c) 160 m (d) 150 m

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction, is (a) 25/11 (b) 3/2 (c) 5/2 (d) 11/5

A certain 8 bit DAC has a regulator of 2mA and an error of 0.5 of full scale reading. The analog output corresponding to binary input of 10101010 is (a) 335345 mA (c) 339.99340.01 mA (b) 337.45342.55 mA (d) 314.5365.5 mA

(a) (6) F 2me me m A ri,Find out the angular frequency of Oscillations of a Particle of mass m which is free to move along a line and attached to a spring whose other end is fixed at a point A, as shown in figure, at a distance from the line. A force F is required to extend the spring to length I. (x

C) D)

Two beads of mass 2m and m can move without are friction along a horizontal wire. They are connected to a fixed wall with two springs of Spring constants 2k and k, as shown in figure. The frequencies of small oscillations are

ONE You are provided with the following - A pendulum bob. - A thread 110cm long - A retort stand, clamp and boss. - Two pieces of wood. - A metre rule. - A stop watch. Proceed as follows: (a) Tie the pendulum bob with the thread provided as shown in Figure 1 . Clamp the end of the thread between the two pieces of wood, so that the length L of the

You are provided with the following: A lens and a lens holder. A screen with cross wires A candle A metre rule. Proceed as follows: a) Arrange the lightened candle, the lens and the screen as shown in figure 2 . Adjust the position of the screen until a sharp inverted image of the candle is formed on the screen. Figure 2 Measure the image

Candle u 30cm www. Lens Screen, L

1. The figure below shows a ray of light incident along the normal. The mirror is rotated at an angle of 15 in a clockwise direction without changing the position of the incident ray, Incident ray Determine the angle through which the reflected ray is rotated. Reflected ray M M (2 marks)

2. Describe how to charge a gold leaf electroscope positively by induction method using a (2 marks) polythene rod and a silk cloth

4. A student set up the circuit shown in figure below. B State the observation when i. Switch S1 is closed S B B3 (S ii. If all switches are closed compare the lighting between B, B2 and B3 (1 mark)

3. An object O is placed in front of a concave mirror as shown in the figure below. Complete the light ray diagram to locate the position of the image. (3 marks)

Two identical loudspeakers are arranged as shown and connected to the same signal generator. Line OR is equidistant from the speakers. An observer moves along line PQ. State and explain the observation. (2 marks) ... If the frequency of sound from the generator is increased, what effect does this have on the interval at which the observer hears

Speaker 1 Speaker 2 R P

The figures below show the profiles of a transverse wave. Fi Determine for the wave the: (i) Wavelength (1mark) . (iii) Velocity

Displacement (mm) 20 10 0 10 20 0.02 s Figure 4 time (s)

9. The diagram below shows a capacitor network connected to a 100V supply. 2F 4F Calculate the total charge in the circuit. H 100V 3F

11. The graph below shows the variation of percentage mass remaining against age in years of a certain radioactive substance Radioactive remaining 100 75 50 25 O 0 Determine the halflife of the source 7 3 5 Age of sample (years) Co 7 (1 mark)

Consider the flat RobertsonWalker metric dt a(t) dx dy dz ds where a(t) is the scale factor. (a) Identify the Killing vectors associated with spatial translations in the metric. 3 marks

a)2Va/L b) 4Va/L c) Va/L d) 6Va/L

An infinite deep one dimensional Square will has x0 and XL. Two small perturbing Potentials of width a and height V are located at x 44 and x 344, where acc toos shown in figure. What will be the difference in the energy shifts between n 2 and n4 chergy due to this perturbation L levels

A particle moves in the onedimensional potential V(x) ax, where a0 is a constant. If the total energy of the particle is E, its time period in a periodic motion is proportional to (a) E13 (b) E12 (c) E3 (d) E2

Two particles of masses m, and m are connected by a massless thread of length L as shown in figure below. oscillations is The particle of mass m on the plane undergoes a circular motion with radius r and angular momentum L. When a small radial displacement (whew E r ) is applied, its radial coordinate is found to found to oscillate about The

The ground state energy of a particle in potential V(x) g(x), estimated using the trail wavefunction (5 (a) y(x) (where g and care constants) is 13 2 15hg 16 2 5(hg (b) ( (ax), 13 (c) x a x a 2 3(hg 13 (d) 7 (g 8 1 ) 13 2

Using the trial function w(x) A(ax), a

A particle of unit mass moves in a potential V(x) ax bx, where a and b are positive constants. The angular frequency of small oscillations about the minimum of the potential is (a) () (c) a 2(2) (b) 2 2(2) (d) 2

A projectile is thrown from a point O on the ground at an angle 45 from the vertical and with a speed of 5 ?2 m/s . The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, t seconds after the splitting, falls to the ground at a

A particle starts sliding down a frictionless inclined plane. If Sn is the distance travelled by it from time t = (n 1) sec to t = n sec, then the ratio S n /S n+1 is (a) (2n 1)/(2n+1) (b) (2n + 1)/2n (c) 2n/(2n + 1) (d) (2n+1)/(2n-1)

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is (a) 4.0 m/s (b) 5.0 m/s (c)5.5 m/s (d) 4.8 m/s

For a body in pure rolling, its rotational kinetic energy is 1/2 times of its translational kinetic energy. The body should be? (a) Solid cylinder (b) Ring (c) Solid sphere (d) Hollow sphere

A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2N on the ring and rolls it without slipping with an acceleration of 0.3 m/s 2 . The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is: (a) 3F/2mR (b) F/3mR (c) F/2mR (d) 2F/3mR

An e.m.f. of 1.5kV is induced in a coil when a current of 4 A collapses uniformly to zero in 8 ms. Determine the inductance of the coil.

A silicon iron ring is wound with 800 turns, the ring having a mean diameter of 120 mm and a crosssectional area of 400 mm. If when carrying a current of 0.5 A the relative permeability is found to be 3000, calculate (a) the self inductance of the coil, (b) the induced c.m.f. if the current is reduced to zero in 80 ms.

An iron ring of mean diameter 10 cm is uniformly wound with 2000 tums of wire. When a current of 0.25 A is passed through the coil a flux density of 0.4 T is set up in the iron. Find (a) the magnetizing force and (b) the relative permeability of the iron under these conditions.

A particle is confined to rotate in a circular path with decreasing linear speed. Then which of the following is correct. (a) angular momentum is conserved about the center. (b) only the direction of L is conserved. (c) it spirals towards the center. (d) its acceleration is towards the center.

A pulley of radius 2 m is rotated about its axis by a force F =20t-5t 2 newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kgm 2 , the number of rotations made by the pulley before its direction of motion it reversed, is (a) more than 6 but less than 9 (b) more than

A Bipolar cascade amplifier, Assume Ia Ic 250 A a) what are the numerical values for Rin, Gm, and Rout b) What is the maximum possible voltage gain Au Use 16 200, V 100V, 4 4000 1

The cascade amplifier of Fig. 8.33 is operated at a current of 0.2 mA with all devices operating at Vov 0.20 V. All devices have V4V. Find g. the output resistance of the amplifier, R. the output resistance of the current source, Rep, the overall output resistance, R., and the voltage gain, A.. VGIO VG30 VG20 0 5 I VDD ls L Q3 Rop(8m303) Fos

n

Consider Bell state of two qubits A and B, (10) A1) B1) A0) B)(101) 10)), and its corresponding density matrix p(). We can think of 10) and 1) as spin12 states 2) and 2), respectively. Find density matrices pA tr(p()), PB trA(p()) Suppose a measurement of o is performed on qubit B. Denote the probabilities of obtaining 1 and 1 as p and p,

Suppose the US and Canada each have 10 units of labor to divide between steel and wheat. If each country had 6 units of labor producing steel and 4 units of labor producing wheat, then the total amount of steel and wheat produced would be Select an answer and submit. For keyboard navigation, use the updown arrow keys to select an answer. 72 units

Calculate the angles at which the first dark band and the next bright band are formed in the Fraunhoffer diffraction pattern of a slit 0.3 mm wide (1. 58904).

Parallel light (5000 A) is normally incident on a single slit. The central maximum fans out at 30 on both sides of the direction of the incident light. Calculate the slit width. For what width of the shit the central maximum would spread out to 90 from the direction of the incident light

Can a thin film of water (1.33) formed on a glass window pane (uy 1.52) act as a nonreflecting film If so, how thick should be the water film

The number of microstates of system of N particles is given by sigma (aUVN)N where U is internal energy, V is volume and a is constant. The pressure P of the system is given by P . UV The value of is

A soap film of 5 x 10 m thick is viewed at an angle of 35 to the normal. Find the wavelengths of light in the visible spectrum, which will be absent from the reflected light. Given the refractive index of the film 1.33.

Question A projectile was fired from the origin O of the Cartesian coordinates on the edge of a cliff with an initial velocity 60 i 175 j The projectile rises first and then falls into the sea at point P, as shown in the following sketch. If you know that the projectile has a time of flight of 40 seconds, that air resistance is neglected, and

Two coherent light waves arrive at a particular point on a screen. The optical path difference between the waves is 3uum. Determine the nature of interference at the point if the wavelength of the wave is 3900 A.

A light wave propagates from a point A to another point B. A glass plate (1.5) of 1 mm thick is introduced in its path. If the wavelength of light is 5000 A. What is the change of phase of the wave at B

The wave function for a light wave is E(z.) 10 sin x (3 x 106 x9 x 1040) (1) Determine the speed, wavelength, frequency and period of the wave. (ii) Determine the magnetic field associated with the wave.

X Two positive charges of 12x 1010 C and 8 10 10 C are placed 10 cm apart. Find the work done in bringing the charges 4 cm closer.

( 7 9). T 1 cm. Find The displacement of particle executing SHM is given by, x 20 sin The period of vibration is 60 seconds. At 10, the displacement of the particle is (a) The initial phase (b) The phase angle when the displacement is 3 cm. (c) The phase difference between any two positions of the particle 10 seconds apart.

The displacement equation of a particle describing simple harmonic motion is x 0.01 sin 100x (1 0.005) meter, where x is the displacement of the particle at any instant 1. Calculate the amplitude, periodic time, maximum velocity and displacement at the time of the motion.

(a) Find the moment of inertia of a Tsection with flange as 150 mm x 50 mm and web as 150 mm x 50 mm about XX and YY axes through the centre of gravity of the section. (b) A Tsection beam has dimensions as shown in Figure. The beam is used as a simply supported beam od span 1.5 m. Calculate the uniformly distributed load (q kNm) which can be

53. An nonrelativistic charged particle moves along the positive xaxis with a constant positive acceleration ax. The particle is at the origin at t 0. Radiation is observed at t 0 at a distant point (0, d, 0) on the yaxis. Which one of the following statements is correct (a) The radiation is unpolarized. (b) The radiation is plane polarized with

A system containing two identical particles is described by a wave function of the form (x)(x) y(x)wp(x) yg Where x and x represent the spatial coordinates of the particles and a and represent all the quantum numbers, including spin, of the states that they occupy. The particles might be (b) Positrons (c) Protons (a) Electrons (d) Deuterons

A Classical model of a diatomic molecule is a springy dumbbell, as shown above, where the dumbbell is free to rotate about axes perpendicular to the spring. In the limit of high temperature, what is the specific heat per mole at constant volume (a) 32 R (b) 52 (c) 72 R (d) 92 R 000000000

The operator a (defind bellow) when operating on a harmonic energy eigenstate y, with energy En produces another energy eigenstate whose energy is Enhoo. Which of the following is true P xi mo a ma 2 I. a commutes with the Hamiltonian. II. a is a Hermitian operator and therefore an observable. III. The adjoint operator a a (a) I only (b) II only

Let a) represent the state of an electron with spin up and 3) the state of an electron with spin down. Valid spin eigenfunctions for a triplet state (S) of a twoelectron atom include which of the following I. a), la), II. (a), Ba) (B)) (a), (B) a), B) III. (a) I only (b) II only (c) III only (d) I and III

Consider electron in graphene obey dispersion relation of electron is proportional to wave vector (k) over the entire kspace, ground state energy per electron of system in term of Fermi energy is (d) EF (b) EF 3

The Coulomb potential V(r) of a hydrogen atom is perturbed by adding H c(y r) (where c is a constant) to the Hamiltonian. The first order correction to the ground state energy is in state 100 (a) c(ao) (b) 4c(ao) (c) 4c(a) (d) none

Consider black body radiation contained in a cavity whose walls are at temperature T. The radiation is in equilibrium with the walls of the cavity. If the temperature of the walls is increased to 2T and the radiation is allowed to come to equilibrium at the new temperature, the number of photon of the radiation increases by a factor of (a)2 (b) 4

If the Pressure of a free electron gas in 2 Dimension is increased by 8 times, its electron density change by (a) 22 (b) 4 (c) 8 (d) 16

(x) The figure above shows one of the possible energy eigenfunctions y(x) for a particle bouncing freely back and forth along the xaxis between impenetrable walls located at x a and x a. The potential energy equals zero for x a. If the energy of the particle is 2 electron volts when it is in the quantum state associated with this eigenfunction,

A very simple square well potential is given 00 x0 V(x) 0 0

The state of a quantum mechanical system is described by a wave function. Consider two physical observables that have discrete eigenvalues observable A with eigenvalues a, and observable B with eigenvalues B. Under what circumstances can all wave functions be expanded in a set of basis states, each of which is a simultaneous eigenfunction of both

The matrix shown above transforms the components of a vector in one coordinate frame S to the components of the same vector in a second coordinates frame S. This matrix represents a rotation of the reference frame S by (a) 30 clockwise about the xaxis (c) 45 clockwise about the zaxis (b) 30 counterclockwise about the zaxis (d) 60 counterclockwise

Two circular hoops, X and Y, are hanging on nails in a wall. The mass of X is four times that of Y, and the diameter of X is also four times that of Y. If the period of small oscillations of X is T, the period of small oscillations of Y is (a) T (b) 72 (c) T4 (d) 78

The magnitude of the Earths gravitational force on a point mass is F(r), where r is the distance from the Earths center to the point mass. Assume the Earth is a homogeneous sphere of radius R. F(R) What is F(2R) (a) 32 (b) 8 (c) 4 (d) 2

Two identical springs with spring constant k are connected to identical masses of mass M, as shown in the figures. The ratio of the period for the springs connected in parallel (Fig. 1) to the period for the springs connected in series (Fig.2) is (a) 12 Figure 1 M (b) 12 Figure 2 M (c) 1 (d) 2

Cucumber contains 99 water. Ramesh buys 100 kg of cucumbers. After 30 days of storing, the cucumbers lose some water. They now contain 98 water. What is the total weight of cucumbers now (a) 99 kg (b) 520 kg (c) 75 kg (d) 2 kg

A student observed the movement of four snails and plots the graphs of distance moved as a function of time as given in figure (A), (B), (C) and (D) Time Time Which of the following is not correct (a) graph (A) (b) graph (B) Time (c) graph (C) Time (d) graph (D)

A vertical pole of length a stands at the centre of a horizontal regular hexagonal ground of side a. A rope that is fixed taut in between a vertex on the ground and the tip of the pole has a length (a) a (b) za (c) 3a (d) a

A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garages rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening