Physics Questions and Answers October 13, 2022

Consider an equilateral triangle with side a having point charges Q at its corners. Compare electric potentials in the center of the triangle and in the middle of its side. What is your expectation Which potential is higher a a2 Vc Vm Q

Find the electric field E(z) along the straight line going between two equal charges Q put at the distance a from each other. Analyze particular cases. Q Q a2 a2 Z 0 E

Charges Q, Q, and 2Q are put at the corners of an equilateral triangle with side a. Find the magnitudes of the forces acting on each charge. 47 13 Q F. 1 12 a 3 2Q F 32

Charges Q are put in the corners of a rectangle with sides a and b. Find the magnitude of the force acting on each charge.

Electric charges Q Q, Q 2Q, and Q3 3Q are placed at r (1,0,0)a, r (0,1,0)a, and r3 (0,0,1)a. Find the electric field E at r (1,1,1)a.

There is a cylinder of mass M that can roll without slipping on a horizontal surface. It is pulled by its center by a cord going over a massless block and then down to the mass m suspended on the cord. Find the linear acceleration of the system, the tension of the cord, and the friction force acting on the cylinder. F T mg

A solid sphere is put on the incline with the angle 8. Find the acceleration of the center of mass of the sphere if it is rolling without slipping. Fo F mg 0 X

A solid cylinder is rolling on a horizontal surface without slipping. Find the ration of its rotational to translational kinetic energies.

Consider the moment of inertia of a system of two masses, m and m, with respect to the axes perpendicular to the line connecting the two masses. Consider the following cases a) the axis goes through the CM of the system b) the axis goes through the mass m c) the axis goes through the mass m. Check if the Steiner theorem holds. b) my XCM L a) m

Two long straight wires are going parallel to each other at the distance a from each other. The wires carry the currents I that go in the same direction. Find the magnetic field created by this system at the center line between the wires (the vertical line on the drawing). 0 A a2 N B B1 B O a2 N

Find the forces acting on the long parallel wires forming an equilateral triangle with a side a in the crosssection. Two currents flow in one direction and one current is flowing in the other direction.

Find the currents and voltages for each of three resistors in the following circuit Ji R 13 R3 it R

In a satellite uplink, the transmitter system has a loss of 1 dB while the transmitter antenna has a gain of 55 dB. There is an atmosphere loss of 2 d8, a free space loss of 200 dB. The receiving antenna has a gain of 20 dB. The receiving system has a bandwidth of 36 MHz and noise temperature of 1000 K. If the desired SNR is 35 dB, compute, (1)

Which of the following expressions correctly describes F

Fill the blanks X, Y and Z to realize the equation F BCD ABC with a 41 multiplexer. OXY0 X 10 1 2 3 41 MUX S1 SO B Y N F

Determine the boolean function that the 8x1 Mutiplexer implements.

What happens to the velocity of a light body when it undergoes an elastic collision in one dimension with a very heavy body at rest? its velocity becomes twice it rebounds with twice of its own velocity it rebounds with its own velocity it stops and comes to rest it does not rebound

A particle travels along a straight line with a speed v = (0.5t 3 - 8t) m/s, where t is in seconds. Determine the acceleration of the particle when t = 2 s.

A lemon kept in water in glass is appears to be bigger than its actual size, when viewed from the sides. This happens because of which phenomenon? Total internal reflection Refraction of light Dispersion Reflection of light None of these

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250N on the surface? 125N 234N 345N 567N 122N

A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy? K 1 = K 2 K 1 > K 2 K 1 < K 2 K 1 ? K 2 K 1 ? K 2

A bullet is shot from a rifle with a speed of 720 m/s. What time is required for the bullet to strike a target 3240 m away? 3.5 s 4.5 s 5.2 s 4.9 s None of these

An insect crawling straight down the length of a meter stick is at the 12cm mark at one instant, and 2 minutes later is at the 60cm mark. Which one of the following is the magnitude of the insect's average velocity? 0.4cm/s 0.5cm/s 24cm/s 30cm/s None of these

Mercury thermometers can be used to measure temperature up to 260C 100C 360C 500C None of these

According to new definition adopted by the "International Astronomical Union" in 2006, which of the following is not a "planet"? Uranus Neptune Pluto Jupiter None of these

The position of the particle is given by s = (2t 2 - 8t + 6) m, where t is in seconds. Determine the time when the velocity of the particle is zero, and the total distance traveled by the particle when t = 3 s.

The position of the particle is given by s (2t2 8t 6) m, where t is in seconds. Determine the time when the velocity of the particle is zero, and the total distance traveled by the particle when t 3 s.

The particle travels from A to B. Identify the three unknowns, and write the three equations needed to solve for them.

The particle travels from A to B. Identify the three unknowns, and write the three equations needed to solve for them.

At a given instant, the football player at A throws a football at C with a velocity of 20 m/s in the direction shown. Determine the constant speed at which the player at B must run so that he can catch the football at the same elevation at which it was thrown. Also calculate the relative velocity and relative acceleration of the football with

At a given instant, the football player at A throws a football at C with a velocity of 20 ms in the direction shown. Determine the constant speed at which the player at B must run so that he can catch the football at the same elevation at which it was thrown. Also calculate the relative velocity and relative acceleration of the football with

At the instant shown, car A travels along the straight portion of the road with a speed of 25 m/s. At this same instant, car B travels along the circular portion of the road with a speed of 15 m/s. Determine the velocity of car B relative to car A.

At the instant shown, car A travels along the straight portion of the road with a speed of 25 ms. At this same instant, car B travels along the circular portion of the road with a speed of 15 ms. Determine the velocity of car B relative to car A.

A car of mass 1300 kg is travelling along a straight level road at 10 ms when the traffic lights change from green to amber. The driver applies the brakes 23 metres from the lights and just manages to stop on the line. Calculate (a) the kinetic energy of the car before braking (b) the work done in bringing the car to rest (c) the force due to the

The flea Spilopsyllus weighs about 0.4 mg and leaves the ground, when it jumps, at about 1 ms. What is its kinetic energy

To move a car of mass 1000 kg along a level road you need to apply a force of about 200 N in the direction of motion to overcome the resistance and get going. If this resistance is 100 N and you push it 20 m, what is the speed of the car

An elastic string of length 1 m is suspended from a fixed point. When a mass of 100 g is attached to the end, its extension is 10 cm. Calculate the energy stored in the string. When an additional 100 g is attached to the end the extension is doubled. How much work is done in producing this extra 10 cm extension

A set of kitchen scales consists of a scale pan supported on a spring as shown. For a particular make of scales the stiffness is 2000 Nm. Find the compression of the spring when measuring 1.5 kg of flour.

An elastic string of natural length 60 cm has one end fixed and a 0.6 kg mass attached to the other end. The system hangs vertically in equilibrium. Find the stiffness of the string if the total length of the string in the equilibrium position is 72 cm.

A car moves along a horizontal road against a resistance of 400 N. What is the greatest speed (in kph) the car can reach if the engine has a maximum power of 16 kW

Two masses 4 kg and 6 kg are attached to the ends of an inextensible string over a pulley. The weights of the string and pulley are much smaller than the two masses attached and so are neglected. The pulley is also assumed to be smooth so that the tension T is the same on both sides of the pulley. The masses are held at the same level and the

calculus physical application:

The electrostatic potential at A arising from a dipole of unit strength at 0, oriented in the direction of the unit vector n, is, in polar coordinates, V(r, 8) (coser), where r A and 0 is the angle between n and A (see Figure 1). Find the divergence of the corresponding electrostatic field E. 0 Fig. 1

A 5 kg mass moves so that its position vector r at time t is given by rsin 2ti cos2t j 2tk. Find (a) the kinetic energy and (b) the work done between t 0 and 1 2.

A particle of mass 3 kg is acted upon by three forces F 1 2k, F 3j4k and F 2i3j. If the particle moves from the point ijk to 3(ij k), find the work done by the resultant.

Find the work done by a force (2i2jk) N which moves a body from the origin to a point P, position vector (i j k) m.

A 15 tonne wagon travelling at 3.6 ms is brought to rest by a buffer (a spring) having a stiffness of 7.5x10 Nm. Assuming that the wagon comes into contact with the buffer smoothly without rebound, calculate the compression of the buffer if there is a constant rolling friction force of 800 N.

In a horizontal pinball machine the spring is compressed 5 cm. If the mass of the ball is 20 g and the stiffness of the spring is 800 Nm what is the speed of the ball when it leaves the spring assuming that friction can be neglected

A 100 g mass is attached to the end B of an elastic string AB with stiffness 16 Nm and natural length 0.25 m, the end A being fixed. The mass is pulled down from A until AB is 0.5 m and then released. Find the velocity of the mass when the string first becomes slack and show that the mass comes to rest when it reaches A.

Ionization potential of hydrogen atom is 13.6eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohrs theory, the spectral lines emitted by hydrogen will be (a) three (b) Four (c) One (d) Two

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is Pa Pa A Oil B (a) 425 kg m

The electric potential at a point in free space due to a charge Q coulomb is Q x 10 volts. The electric field at that point is (a) 4 , Qx10 voltm (c) 4 E Qx102 voltm (b) 12 Qx1020 voltm (d) 12 T Qx102 voltm

What is the value of inductance L for which the current is maximum in a series LCR circuit with C 10 F and c 1000s (a) 1 mH (b) cannot be calculated unless R is known (c) 10 mH (d) 100 mH

The electric field associated with an e.m. wave in vacuum is given by E 140 cos (kz 6 10t), where E, z and t are in voltm, meter and seconds respectively. The value of wave vector k is (a) 2 m (c) 6 m (b) 0.5 m (d) 3 m

length of the chain that can hang over one edge of the table is (a) 20 (c) 35 (b) 25 (d) 15,A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the

What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 10 J by the end of the second revolution after the beginning of the motion (a) 0.1 ms (c) 0.18 ms (b) 0.15 ms (d) 0.2 ms

A Carnot engine whose efficiency is 50 has an exhaust temperature of 500 K. If the efficiency is to be 60 with the same intake temperature, the exhaust temperature must be (in K) (a) 800 (c) 400 (b) 200 (d) 600

In the circuit shown in the figure, if potential at point A is taken to be zero, the potential at point B is 2V R 1A R (a)IV (b) 2V (c)2V (d) IV IV IA C 2A B 2A

Two identical thin planoconvex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is (a) 25 cm (c) 50 cm (b)50 cm (d) 20 cm

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P. The instantaneous velocity of this car is proportional to (a) tP 0 12 (c) t (b) t2 (d)

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. P(in kPa) 2 B V(in m) The change in internal energy of the gas during the transition is (a) 20 kJ (c)12 kJ (b) 20 J (d) 20 kJ

If power dissipated in the 922 resistor in the circuit shown is 36 watt, the potential difference across the 20 resistor is (a) 4 volt (c) 10 volt 4 902 wwww 652 ww wwww 202 (b) 8 volt (d) 2 volt

The refracting angle of a prism is A, and refractive index of the material of the prism is cot(A2). The angle of minimum deviation is 2015 (a) 180 2A (c) 180 2A (b) 90 A (d) 180 3A

Youngs double slit experment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive index of the medium is nearly (a) 1.59 (c) 1.78 (b) 1.69 (d) 1.25

In a common emitter (CE) amplifier having a voltage gain G, the transistor used has transconductance 0.03 mho and current gain 25. If the above transistor is replaced with another one with transconductance 0.02 mho and current gain 20, the voltage gain will be (a) 1.5 G (b) G (c) G (d) G

The period of oscillation of a mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be (a) T (b) 2 (c) 2T (d) 2 T

To get output 1 for the following circuit, the correct choice for the input is A B (a) A 0, B 1, C 0 (c) A 1, B 1, C 0 D (b) A 1, B 0, C 0 (d) A 1, B 0, C 1

A particle of mass m 5 is moving with a uniform speed v 32 in the XOY plane along the line y x 4. The magnitude of the angular momentum of the particle about the origin is (a) 60 units (c) zero (b) 402 units (d) 7.5 units

A particle, with restoring force proportional to displacement and resistve force proportional to velocity is subjected to a force F sin o. If the amplitude of the particle is maximum for 0, and the energy of the particle is maximum foro , then (a) o, (c) o, o, and w w, o, and o 0, 0 (b) (d) , 0, and a 0, , , and w 0, 0

A 200 W sodium street lamp emits yellow light of wavelength 0.6 um. Assuming it to be 25 efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is (a) 1.5 1020 (c) 62 1020 (b) 6 x 108 (d) 3 10

A car covers the first half of the distance between other half at 60 kmh. The two places at 40 kmh and average speed of the car is (a) 40 kmh (c) 50 kmh (b) 48 kmh (d) 60 kmh

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle 0 without slipping and slipping down the incline without rolling is (a) 57 (c) 25 (b) 23 (d) 75

3 F A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR, and RQ are F, F, and F, respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is (a) F,FF (b) (F3F) F (c) (F3F) F (d) F F,F, 3 2 2 R

A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 kmh and 40 kmh respectively. The velocity of the car midway between P and Q is (a) 33.3 km h (c) 252 kmh (b) 202 kmh (d) 35 kmh

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g, then 2005 (a) g g9 (b) g 27g (c) g9g (d) g3g

A bar magnet having a magnetic moment of 2 10 JT is free to rotate in a horizontal plane. A horizontal magnetic field B 6 10 T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60 from the field is (a) 12 J (b) 6 J (d) 0.6 J (c) 2 J

If a vector 21 3 8k is perpendicular to the vector 4 4 ak, then the value of a is (b)12 (d)1 (a) 12 (c) 1

A source and an observer move away from each other, with a velocity of 10ms with respect to ground. If the observer finds the frequency of sound coming from the source as 1950 Hz, then original frequency of source is (velocity of sound in air 340 ms) (b) 2068 Hz (d) 2486 Hz (a) 1950 Hz (c) 2132 Hz

The total energy of an electron in the first excited state of hydrogen atom is about 3.4 eV. Its kinetic energy in this state is (a) 3.4 eV (c)3.4 eV (b) 6.8 eV (d) 6.8 eV

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectiles is (a) 0 tan() (b) 0 tan (4) (c) 0 tan (2) (d) 0 45

Two nonmixing liquids of densities p and np (n 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL(p 1) in the denser liquid. The density d is equal to 2016 (a) 1 (n 1)pp (b) 2 (n 1)pp (c) 2 (n1)pp (d) 1 (n1)pp

From a point charge, there is a fixed point A. At A, there is an electric field of 500 Vm and potential difference of 3000 V. Distance between point charge and A will be (a) 6 m (c) 16 m (b) 12 m (d) 24 m

A nucleus 4X has mass represented by M(A, Z). If M and M denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then (a) B.E. n ZM (A Z)M M(A, Z)c P n (b) B.E. ZM ZM M(A, Z)c (c) B.E. M(A, Z) ZM(A Z)M (d) B.E. M(A, Z)ZM(A Z)Mc P

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to (a) the speed of light in vacuum (b) reciprocal of speed of light in vacuum (c) the ratio of magnetic permeability to the electric susceptibility of vacuum (d) unity

Radioactive material A has decay constant 8 and material B has decay constant 2. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material B to that A will be 17181912

Starting from rest, a body slides down a 45 inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is (a) 0.80 (c) 0.25 (b) 0.75 (d) 0.33

The masses of the three wires of copper are in the ratio of 135 and their lengths are in the ratio of 5 3 1. The ratio of their electrical resistance is (a) 135 (c) 125 125 (b) 531 (d) 125 151

A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices and and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is R (a) (b) (c) (d) 2(HH) R (HH) 2R (HH) R 2(H)

C and Si both have same lattice structure, having 4 bonding electrons in each. However, C is insulator whereas Si is intrinsic semiconductor. This is because (a) In case of C the valence band is not completely filled at absolute zero temperature. (b) In case of C the conduction band is partly filled even at absolute zero temperature. (c) The four

A current of 3 amp flows through the 202 resistor shown in the circuit. The power dissipated in the 5 resistor is (a) 4 watt (c) 1 watt 2W 1W W 4W www ww 5W (b) 2 watt (d) 5 watt

What is the total charge passing through the X-ray tube per second?

A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47, respectively. Blue Green Red 45 The prism will (a) separate all the three colours from one another (b) not separate the three colours

Prove, by integration, that the work done in stretching an elastic string, of natural length / and modulus of elasticity A, from length / to a length 1+x is 21 A particle of mass m is suspended from a fixed point O by a light elastic string of natural length I. When the mass hangs freely at rest the length of the string is 131. The particle is now

What is the beam current density of the X-ray tube in Amperes per square centimeter?

The intensity at the maximum in a Youngs double slit experiment is I. Distance between two slits is d 52, where is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance D 10 d (a) I (c) lo (b) (d)

What is the total energy of X-rays produced by the X-ray tube per second in joules?

One end of an elastic string of modulus 20 mg and natural length a is attached to a point A on the surface of a smooth plane inclined at an angle of 30 to the horizontal. The other end is attached to a particle P of mass m. Initially P is held at rest at A and then released so that it slides down a line of greatest slope of the plane. By use of

What is the total number of X-ray photons produced by the X-ray tube per second?

What is the power output of the X-ray tube in watts?

A train of mass 106 kg starts from rest and moves up a slope which is inclined at an angle arcsin (1/250) to the horizontal. Throughout its motion, the train's engines work at a power of 106 W and the train experiences a variable resistance. After 15 minutes, the train is moving with speed 20 ms and has travelled a distance of 15 km along the

What is the energy of each X-ray photon in electron volts as it is produced?

What is the frequency of the X-rays produced by the electrons as they strike the target?

(In this question you should assume g is 9.8 ms) A lorry has mass 6 tonnes (6000 kg) and its engine can develop a maximum power of 10 kW. When the speed of the lorry is v ms the total non-gravitational resistance to motion has magnitude 25v N. Find the maximum speed of the lorry when travelling (a) along a straight horizontal road, (b) up a hill

d) (i) Deduce the Lorentz-Fitzerald contraction (6 Marks) (ii) 8. A rod has a length of 1 metre. If the ros is placed inside a satellite moving with a velocity of 0.8c relative to the laboratory, what is the length of the rod as determined by the observer in the laboratory.(5 MARKS)

Determine the maximum number of electrons that can be accommodated in an atom with the 3P orbital as the highest energy level orbital