Physics

### (i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.β = √(n-1)k1 u/v / u + v

i) Time taken by the ray to travel from S to P1 is = t1 = √u2 + b2/c Time taken by the ray to travel from P1 to O is = t2 = v/c (1+ ½ b2/v2) Time taken to travel through the lens is =...

### Show that for a material with refractive index µ ≥ 2 , light incident at any angle shall be guided along a length perpendicular to the incident face. Answer:

Let the refractive index of the rectangular slab be μ ≥ √2. μ = 1/sin ic sin ic > 1/ μ cos r ≥ 1/ μ sin i/sin r = μ From Snell’s law Sin I = μ sin r i = 90o 1 + 1 ≤ μ2 2 ≤ μ2 Taking the square...

### A jar of height h is filled with a transparent liquid of refractive index µ. At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmetrically about the centre, the dot is invisible.

tan ic d/2/h ic = d/2h d = 2h tan ic d = 2h ×1/√μ2 – 1

### A short object of length L is placed along the principal axis of a concave mirror away from focus. The object distance is u. If the mirror has a focal length f, what will be the length of the image? You may take L << |v-f|

The mirror formula is 1/v + 1/u = 1/f u is the object distance v is the image distance du = |u1 – u2| = L Differentiating on the both sides we get, dv/v2 = -du/u2 v/u = f/u-f du = L, therefore,...

### For a glass prism (µ = √3 ) the angle of minimum deviation is equal to the angle of the prism. Find the angle of the prism.

μ = sin[(A + δm)/2]/sin (A/2)

### An astronomical refractive telescope has an objective of focal length 20m and an eyepiece of focal length 2cm.(a) The length of the telescope tube is 20.02m. (b) The magnification is 1000. (c) The image formed is inverted. (d) An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.

Answer: (a) The length of the telescope tube is 20.02m. (b) The magnification is 1000. (c) The image formed is inverted.                      ...

### A magnifying glass is used, as the object to be viewed can be brought closer to the eye than the normal near point. This results in(a) a larger angle to be subtended by the object at the eye and hence viewed in greater detail.(b) the formation of a virtual erect image.(c) increase in the field of view.(d) infinite magnification at the near point.

Answer: (a) a larger angle to be subtended by the object at the eye and hence viewed in greater detail. (b) the formation of a virtual erect image.              ...

### Between the primary and secondary rainbows, there is a dark band known as Alexandar’s dark band. This is because(a) light scattered into this region interfere destructively.(b) there is no light scattered into this region(c) light is absorbed in this region.(d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and 50°.

Answer: (a) light scattered into this region interfere destructively. (d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately 42° and...

### A rectangular block of glass ABCD has a refractive index 1.6. A pin is placed midway on the face AB. When observed from the face AD, the pin shall (a) appear to be near A.(b) appear to be near D.(c) appear to be at the centre of AD.(d) not be seen at all.

Answer: (a) appear to be near A. (d) not be seen at all. The pin will appear to be near A as long as the angle of incidence on AD of the ray emerging from the pin is smaller...

### Consider an extended object immersed in water contained in a plane trough. When seen from close to the edge of the trough the object looks distorted because(a) the apparent depth of the points close to the edge is nearer the surface of the water compared to the points away from the edge.(b) the angle subtended by the image of the object at the eye is smaller than the actual angle subtended by the object in the air.(c) some of the points of the object far away from the edge may not be visible because of total internal reflection.(d) water in a trough acts as a lens and magnifies the object.

Answer: (a) the apparent depth of the points close to the edge is nearer the surface of the water compared to the points away from the edge. (b) the angle subtended by the image of the object at the...

### A car is moving with at a constant speed of 60 km h–1 on a straight road. Looking at the rearview mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km h –1. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 still the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?(a) The speed of the car in the rear is 65 km h–1.(b) In the side mirror, the car in the rear would appear to approach with a speed of 5 km h–1 to the driver of the leading car.(c) In the rearview mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.(d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

Answer: (d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

### The optical density of turpentine is higher than that of water while its mass density is lower. The figure shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in the figure, the path shown is correct?a) 1b) 2c) 3d) 4

Answer: b) 2 When light travels from (optically) rarer medium air to optically denser medium turpentine, it bends towards the normal, i.e., θ1 >...

### The direction of a ray of light incident on a concave mirror as shown by PQ while directions in which the ray would travel after reflection is shown by four rays marked 1, 2, 3, and 4. Which of the four rays correctly shows the direction of reflected ray?a) 1b) 2c) 3d) 4

Answer: b) 2 After reflection, the ray PQ of light that passes through focus F and strikes the concave mirror should become parallel to the primary...

### The phenomena involved in the reflection of radiowaves by ionosphere is similar toa) reflection of light by a plane mirrorb) total internal reflection of light in the air during a miragec) dispersion of light by water molecules during the formation of a rainbowd) scattering of light by the particles of air

Answer: b) total internal reflection of light in the air during a mirage The ionosphere, a layer of the atmosphere, reflects radio waves, allowing them to reach far-flung portions of the globe....

### The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it willa) act as a convex lens only for the objects that lie on its curved sideb) act as a concave lens only for the objects that lie on its curved sidec) act as a convex lens irrespective of the side on which the object liesd) act as a concave lens irrespective of the side on which the object lies

Answer: c) act as a convex lens irrespective of the side on which the object lies

### A passenger in an aeroplane shalla) never see a rainbowb) may see a primary and a secondary rainbow as concentric circlesc) may see a primary and a secondary rainbow as concentric arcsd) shall never see a secondary rainbow

Answer: b) may see a primary and a secondary rainbow as concentric circles As an aeroplane flies higher in the sky, passengers may notice a primary and secondary rainbow in the form of concentric...

### An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The imagea) moves away from the lens with a uniform speed 5 m/sb) moves away from the lens with a uniform accelerationc) moves away from the lens with a non-uniform accelerationd) moves towards the lens with a non-uniform acceleration

Answer: c) moves away from the lens with a non-uniform acceleration In our case, the object approaches a convergent lens from the left at a uniform speed of 5 m/s, causing the image to travel away...

### A short pulse of white light is incident from air to a glass slab at normal incidence. After travelling through the slab, the first colour to emerge isa) blueb) greenc) violetd) red

Answer: d) Red The relation v = fλ describes the velocity of a wave. The frequency of light does not change when it travels from one medium to another. As a result, the bigger the wavelength, the...

### Equipotential surfaces a) are closer in regions of large electric fields compared to regions of lower electric fields b) will be more crowded near sharp edges of a conductor c) will be more crowded near regions of large charge densities d) will always be equally spaced

The correct answer is a) are closer in regions of large electric fields compared to regions of lower electric fields b) will be more crowded near sharp edges of a conductor c) will be more crowded...

### Consider a uniform electric field in the z direction. The potential is a constant a) in all space b) for any x for a given z c) for any y for a given z d) on the x-y plane for a given z

The correct answer is b) for any x for a given z c) for any y for a given z d) on the x-y plane for a given z

### A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d1 and dielectric constant k1 and the other has thickness d2 and dielectric constant k2 as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness d = d1 + d2 and effective dielectric constant k. The k is a) k1d1 + k2d2/d1+d2 b) k1d1 + k2d2/k1 + k2 c) k1k2 (d1 + d2)/(k1d1 + k2d2) d) 2k1k2/k1 + k2

The correct answer is c) k1k2 (d1 + d2)/(k1d1 + k2d2)

### Equipotential at a great distance from a collection of charges whose total sum is not zero are approximately a) spheres b) planes c) paraboloids d) ellipsoids

The correct answer is a) spheres

### The electrostatic potential on the surface of a charged conducting sphere is 100V. Two statements are made in this regard: S1: At any point inside the sphere, the electric intensity is zero S2: At any point inside the sphere, the electrostatic potential is 100V Which of the following is a correct statement? a) S1 is true but S2 is false b) Both S1 and S2 are false c) S1 is true, S2 is also true, and S1 is the cause of S2 d) S1 is true, S2 is also true but the statements are independent

The correct answer is c) S1 is true, S2 is also true, and S1 is the cause of S2

### Figure shows some equipotential lines distributed in space. A charged object is moved from point A to point B. a) the work done in fig (i) is the greatest b) the work done in fig (ii) is least c) the work done is the same in fig (i), fig (ii), and fig (iii) d) the work done in fig (iii) is greater than fig (ii) but equal to that in fig (i)

The correct answer is c) the work done is the same in fig (i), fig (ii), and fig (iii)

### A capacitor of 4μF is connected as shown in the circuit. The internal resistance of the battery is 0.5Ω. The amount of charge on the capacitor plates will be a) 0 b) 4μC c) 16μC d) 8μC

The correct answer is d) 8μC

### A ball is dropped and its displacement vs time graph is as shown in the figure where displacement x is from the ground and all quantities are positive upwards. a) Plot qualitatively velocity vs time graph b) Plot qualitatively acceleration vs time graph

a) At t=0 and v=0 , v-t graph is: b) At x = 0, a-t graph is:

### A positively charged particle is released from rest in a uniform electric field. The electric potential energy of the charge a) remains a constant because the electric field is uniform b) increases because the charge moves along the electric field c) decreases because the charge moves along the electric field d) decreases because the charge moves opposite to the electric field

The correct answer is c) decreases because the charge moves along the electric field

### A certain mass of hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is: (given 1u = 931 MeV)

Option A 13.35 MeV Option B 2.67 MeV Option C 26.7 MeV Option D 6.675 MeV Solution: The correct option is Option D The energy released per u is given by:

### In a common emitter (CE) amplifier having a voltage gain G, transistor used has trans conductance 0.02 mho and current gain 20, the voltage gain will be

Option A  5/4 G Option B  2/3 G Option C 1.5 G Option D 1/3 G Solution: The correct answer is Option B 2/3G

### If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earths radius?

Answer: We know that the distance or range of transmission tower is given by the expression: $dT=\sqrt{2{{h}_{T}}R}$ R represents the radius of the earth (approximately 6400 km). hT​ denotes the...

### A TV transmission tower antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is

(i) at ground level, (ii) at a height of 25 m? Calculate the percentage increase in area covered in case (ii) relative to case (i). Answer: We know that: ${{R}_{e}}=6.4\times {{10}^{6}}m$ The...

### Figure shows a communication system. What is the output power when the input signal is of 1.01mW? (gain in dB = 10 log10 (Po /Pi ).

Answer: It is given that there is a loss of signal 2dB per km. So total loss suffered in 5km = -2 x 5 = -10 dB. In both input and output amplifiers, the total gain of the signal is given by: =...

### Why is an AM signal likely to be noisier than an FM signal upon transmission through a channel?

Answer: In an amplitude modulated wave, the carrier wave's instantaneous voltage varies. As a result, assuming noise as a part of the modulated signal, a noise signal can be added and received...

### A 1 KW signal is transmitted using a communication channel which provides attenuation at the rate of – 2dB per km. If the communication channel has a total length of 5 km, the power of the signal received is [gain in dB = 10 log P0/P1]

(a) 900 W (b) 100 W (c) 990 W (d) 1010 W Answer: The correct option is (b) 100 W Explanation: According to the question, Pi​ =1 kW = 1000W The rate of attenuation of the signal = -2dB/km Length of...

### A 100m long antenna is mounted on a 500m tall building. The complex can become a transmission tower for waves with λ

(a) ~ 400 m (b) ~ 25 m (c) ~ 150 m (d) ~ 2400 m Answer: The correct option is (a) ~ 400 m Explanation: According to the question, the length of building ois l = 500m and Length of antenna is 100m...

### Three waves A, B and C of frequencies 1600 kHz, 5 MHz and 60 MHz, respectively are to be transmitted from one place to another. Which of the following is the most appropriate mode of communication:

(a) A is transmitted via space wave while B and C are transmitted via skywave (b) A is transmitted via ground wave, B via skywave and C via space wave (c) B and C are transmitted via ground wave...

### In the circuit, find the value of RC.

Answer: Ie = Ic + Ib IcRc + Vce + IeRe = Vcc Rib + Vbe + IeRe = Vcc Ib = 11.5/200 mA Rc + Re = 1.56 kilo ohm Rc = 560 Ohm

### For the transistor circuit shown in Fig.14.19, evaluate VE, RB, RE given IC = 1 mA, VCE = 3V, VBE = 0.5 V and VCC = 12 V, β = 100.

Answer: ${{I}_{C}}={{I}_{B}}+{{I}_{E}}$ ${{I}_{B}}<<<{{I}_{C}}$ $\therefore {{I}_{C}}={{I}_{E}}$ ${{I}_{C}}=1mA(given)$ $\therefore {{I}_{C}}={{I}_{E}}=1mA$ By Kirchhoff's loop...

### Consider a box with three terminals on top of it:

Three components namely, two germanium diodes and one resistor are connected across these three terminals in some arrangement. A student performs an experiment in which any two of these three...

### An X-OR gate has the following truth table:

A B Y 0 0 0 0 1 1 1 0 1 1 1 0 It is represented by the following logic relation Build this gate using AND, OR, and NOT gates. Answer: In given logic relation Y = AˉB + ABˉ =Y1​Y2​ Now, the logic...

### Suppose a ‘n’-type wafer is created by doping Si crystal having 5 × 1028 atoms/m3 with 1ppm concentration of As. On the surface 200 ppm Boron is added to create the ‘P’ region in this wafer. Considering ni = 1.5 × 1016 m–3,

(i) Calculate the densities of the charge carriers in the n & p regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when the diode is reverse...

### An electron (mass m) with an initial velocity. If = , it’s de Broglie wavelength at time t is given bya) b) c) d )

The correct answer is c)$\frac{\lambda_{0}}{\sqrt{1+\frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}$ The de Broglie equation h=mv describes the relationship between a moving particle's momentum...

### An electron (mass m ) with an initial velocity It’s de Broglie wavelength at time t is given bya) b) c) d)

The correct answer is a) $\frac{\lambda_{0}}{1+\frac{e E_{0}}{m} \frac{t}{v_{0}}}$ The wave associated with moving particle is called matter wave or de-Broglie wave and it propagates in the form of...

### Consider the circuit arrangement in which the input and output characteristics of NPN transistor in CE configuration

Select the values of RB and RC for a transistor whose VBE = 0.7 V, so that the transistor is operating at point Q as shown in the characteristics shown in the figure (b). Given that the input...

### Assuming the ideal diode. Explain the waveform.

Answer: When signal 20sinωt provides an input voltage less than 5 volt (because after 5V, the diode will receive a positive voltage at its P-junction), the diode will be in reverse bias, and the...

### Write the truth table for the circuit shown in the figure. Name the gate that the circuit resembles.

Answer: The given circuit is AND and the truth table is: A B X = A.B 0 0 0 0 1 0 1 0 0 1 1 1

### Explain why elemental semiconductor cannot be used to make visible LEDs.

Answer:  The bandgap in an elemental conductor is such that the emissions are infrared rather than visible. Elemental semiconductors cannot be used to make visible LEDs. This is because the energy...

### How would you set up a circuit to obtain NOT gate using a transistor?

Answer: a) There is only one input and only one output b) By making use of the Boolean expression c) Realization of NOT gate d) Making use of the truth table The NOT gate is a single-input,...

### Two car garages have a common gate which needs to open automatically when a car enters either of the garages or cars enter both. Devise a circuit that resembles this situation using diodes for this situation.

Answer: When an automobile approaches the gate, one or both gates are open. As a result, the OR gate produces the required result. The following is a truth table for the same: A B Y = A + B 0 0 0 0...

### If the resistance R1 is increased, how will the readings of the ammeter and voltmeter change?

Answer: From the circuit diagram, we have IbR1 + Vbe = Vbb Expression for the base current gives us Ib = Vbb – Vbe/R1 It can be seen that Ib is inversely proportional to R1 The reading of the...

### Three photodiodes D1, D2 and D3 are made of semiconductors having band gaps of 2.5eV, 2eV and 3eV, respectively. Which ones will be able to detect light of wavelength 6000 Ao?

Answer: According to the question, the wavelength is: λ = 6000 Ao = 6000 × 10-10m Expression for the energy of the light photon is as follows: E = hc/ λ Upon substituting the values of h, c and...

### (i) Name the type of a diode whose characteristics are shown in the figure (a) and in the figure (b)

(ii) What does the point P in the figure (a) represent? (iii) What does the points P and Q in the figure (b) represent? Answer: (i) Figure a) depicts the Zener diode's characteristics, whereas...

### In a CE transistor amplifier there is a current and voltage gain associated with the circuit. In other words, there is a power gain. Considering power a measure of energy, does the circuit violate conservation of energy?

Answer: The DC supply is connected to the CE transistor amplifier to provide energy to the signal. As a result, the CE configuration amplifier has a significant power gain. The extra power necessary...

### The amplifiers X, Y and Z are connected in series. If the voltage gains of X, Y and Z are 10, 20 and 30, respectively and the input signal is 1 mV peak value, then what is the output signal voltage (peak value)

(i) if dc supply voltage is 10V? (ii) if dc supply voltage is 5V? Answer: According to the question, we can write Voltage gain in X = vx = 10 Voltage gain in Y = vy = 20 Voltage gain in Z = vz = 30...

### Draw the output waveform across the resistor in the figure.

The waveform formed across the resistance diode conducts when the diode is forward biassed in the given circuit, hence the output will be only when the input +1V is between t1 and t2. As a result,...

### Can the potential barrier across a p-n junction be measured by simply connecting a voltmeter across the junction?

Answer: We can't use a voltmeter to detect the potential barrier across a p-n junction because the voltmeter's resistance must be very high relative to the junction resistance, which is almost...

### Sn, C, and Si, Ge are all group XIV elements. Yet, Sn is a conductor, C is an insulator while Si and Ge are semiconductors. Why?

Answer: If there is no energy gap between the conduction and valence bands in an atom's energy band diagram, the material will conduct current. This energy gap narrows when the material transitions...

### Why are elemental dopants for Silicon or Germanium usually chosen from group XIII or group XV?

Answer: Because the size of the dopant must be compatible with the semiconductor and they must form covalent bonds. The elemental dopants for silicon or germanium are usually chosen from groups XIII...

### The breakdown in a reverse-biased p–n junction diode is more likely to occur due to

(a) large velocity of the minority charge carriers if the doping concentration is small (b) large velocity of the minority charge carriers if the doping concentration is large (c) strong electric...

### To reduce the ripples in a rectifier circuit with capacitor filter

(a) RL should be increased (b) input frequency should be decreased (c) input frequency should be increased (d) capacitors with high capacitance should be used Answer: The correct options are: (a) RL...

### What happens during regulation action of a Zener diode?

(a) The current in and voltage across the Zenor remains fixed (b) The current through the series Resistance (Rs ) changes (c) The Zener resistance is constant (d) The resistance offered by the Zener...

### In the depletion region of a diode

(a) there are no mobile charges (b) equal number of holes and electrons exist, making the region neutral (c) recombination of holes and electrons has taken place (d) immobile charged ions exist...

### In an NPN transistor circuit, the collector current is 10mA. If 95 per cent of the electrons emitted reaches the collector, which of the following statements are true?

(a) The emitter current will be 8 mA (b) The emitter current will be 10.53 mA (c) The base current will be 0.53 mA (d) The base current will be 2 mA Answer: The correct options are: (b) The emitter...

### In the figure shows the transfer characteristics of a base biased CE transistor. Which of the following statements are true?

(a) At Vi = 0.4V, transistor is in active state (b) At Vi = 1V, it can be used as an amplifier (c) At Vi = 0. .5V, it can be used as a switch turned off (d) At Vi = 2.5V, it can be used as a switch...

### Consider an NPN transistor with its base-emitter junction forward biased and collector-base junction reverse biased. Which of the following statements are true?

(a) Electrons crossover from emitter to collector (b) Holes move from base to collector (c) Electrons move from emitter to base (d) Electrons from emitter move out of base without going to the...

### When an electric field is applied across a semiconductor

(a) electrons move from lower energy level to higher energy level in the conduction band (b) electrons move from higher energy level to lower energy level in the conduction band (c) holes in the...

### Truth table for the given circuit in the figure is

(a) A B E 0 0 1 0 1 0 1 0 1 1 1 0 (b) A B E 0 0 1 0 1 0 1 0 0 1 1 1 (c) A B E 0 0 0 0 1 1 1 0 0 1 1 1 (d) A B E 0 0 0 0 1 1 1 0 1 1 1 0 Answer: The correct option is (c) A B E 0 0 0 0 1 1 1 0 0 1 1...

### In the circuit shown in the figure, if the diode forward voltage drop is 0.3 V, the voltage difference between A and B is

(a) 1.3 V (b) 2.3 V (c) 0 (d) 0.5 V Answer: The correct option is (b) 2.3 V Explanation: Let V represent the potential difference between A and B, then we can write: V - 0.3 = (5 +5) x 103 x (0.2 x...

### The output of the given circuit in the figure

(a) would be zero at all times (b) would be like a half-wave rectifier with positive cycles in output (c) would be like a half-wave rectifier with negative cycles in output (d) would be like that of...

### Hole is

(a) an anti-particle of the electron (b) a vacancy created when an electron leaves a covalent bond (c) absence of free electrons (d) an artificially created particle Answer: The correct option is...

### Why do stable nuclei never have more protons than neutrons?

Because protons are charged particles that resist one other, stable nuclei never have more protons than neutrons. Because of the strong repulsion, extra neutrons only produce attractive forces,...

### Which one of the following cannot emit radiation and why? Excited nucleus, excited electron.

Because the energy of the electronic energy level is in the eV range rather than the MeV range, an excited electron cannot release radiation.

### Draw a graph showing the variation of decay rate with number of active nuclei.

According to Rutherford and Soddy law, the radioactive decay is given as –dN/dt = λN.

### The variation of the decay rate of two radioactive samples A and B with time is shown in the figure. Which of the following statements are true?

(a) The decay constant of A is greater than that of B, hence A always decays faster than B (b) The decay constant of B is greater than that of A but its decay rate is always smaller than that of A...

### Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact:(a) nuclear forces have short-range(b) nuclei are positively charged(c) the original nuclei must be completely ionized before fusion can take place(d) the original nuclei must first break up before combining with each other

The correct options are: (a) nuclear forces have short-range (b) nuclei are positively charged

### Heavy stable nuclei have more neutrons than protons. This is because of the fact that(a) neutrons are heavier than protons(b) electrostatic force between protons are repulsive(c) neutrons decay into protons through beta decay(d) nuclear forces between neutrons are weaker than that between protons

The correct option is: (b) electrostatic force between protons are repulsive

### The gravitational force between an H-atom and another particle of mass m will be given by Newton’s law: , where r is in km and(a) M = mproton + m electron(b) M = mproton melectron (c) M is not related to the mass of the hydrogen atom(d) M = mproton +melectron magnitude of the potential energy of electron in the -atom)

The correct option is: (b) M = mproton $+$ melectron $-B / c^{2}(B=13.6 \mathrm{eV})$

### What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant. What geometrical characteristics of the LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

When the distance between two points is doubled, the intensity of light is reduced by one-fourth. Geometrical characteristics of the LASER are: a) unidirectional b) monochromatic c) coherent...

### Electromagnetic waves with wavelengthi) is used in satellite communicationii) is used to kill germs in water purifiesiii) is used to detect leakage of oil in underground pipelinesiv) is used to improve visibility in runaways during fog and mist conditionsa) identify and name the part of the electromagnetic spectrum to which these radiations belongb) arrange these wavelengths in ascending order of their magnitudec) write one more application of each

a) i) $\lambda_{1}$ is a microwave, used in satellite communication. ii) $\lambda_{2}$ is UV rays, used in a water purifier for killing germs. iii) $\lambda_{3}$ is X-rays, used in improving the...

### Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in the figure.A polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid (a) For a particular orientation, there shall be darkness as observed through the polaroid (b) The intensity of light as seen through the polaroid shall be independent of the rotation (c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid (d) The intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid

The correct answer is c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid

### Consider sunlight incident on a slit of width 104 A. The image seen through the slit shall (a) be a fine sharp slit white in colour at the centre (b) a bright slit white at the centre diffusing to zero intensities at the edges (c) a bright slit white at the centre diffusing to regions of different colours (d) only be a diffused slit white in colour

The correct answer is (a) be a fine sharp slit white in colour at the centre

### In a Young’s double-slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there shall be alternate interference patterns of red and blue (b) there shall be an interference pattern for red distinct from that for blue (c) there shall be no interference fringes (d) there shall be an interference pattern for red mixing with one for blue

The correct answer is c) there shall be no interference fringes

### Two sources S1 and S2 of intensity I 1 and I 2 are placed in front of a screen in the figure (a). The pattern of intensity distribution seen in the central portion is given by the figure (b). In this case which of the following statements are true;(a) S1 and S2 have the same intensities (b) S1 and S2 have a constant phase difference (c) S1 and S2 have the same phase (d) S1 and S2 have the same wavelength.

The correct answer is a) S1 and S2 have the same intensities b) S1 and S2 have a constant phase difference c) S1 and S2 have the same phase

### Consider sunlight incident on a pinhole of width 103A. The image of the pinhole seen on a screen shall be (a) a sharp white ring (b) different from a geometrical image (c) a diffused central spot, white in colour (d) diffused coloured region around a sharp central white spot

The correct answer is b) different from a geometrical image d) diffused coloured region around a sharp central white spot

### Consider the diffraction pattern for a small pinhole. As the size of the hole is increased (a) the size decreases (b) the intensity increases (c) the size increases (d) the intensity decreases

The correct answer is a) the size decreases b) the intensity increases

### For light diverging from a point source (a) the wavefront is spherical (b) the intensity decreases in proportion to the distance squared (c) the wavefront is parabolic (d) the intensity at the wavefront does not depend on the distance

The correct answer is a) the wavefront is spherical b) the intensity decreases in proportion to the distance squared

### Is Huygen’s principle valid for longitudinal sound waves?

For longitudinal sound waves, Huygen's concept holds true.

### Consider a point at the focal point of a convergent lens. Another convergent lens of short focal length is placed on the other side. What is the nature of the wavefronts emerging from the final image?

Wavefront and ray orientations are perpendicular to each other. L1 is the source of parallel rays that produce I2 at the focal length of the lens in the diagram above. The created picture serves as...

### What is the shape of the wavefront on earth for sunlight?

The distance between the sun and the earth is known to be enormous. We also know that the sun is spherical and that it may be thought of as a point source of light that can be seen from a great...

### Professor C.V.Raman surprised his students by suspending freely a ting light ball in a transparent vacuum chamber by shining a laser beam on it. Which property of EM waves was he exhibiting? Give one more example of this property.

Professor CV Raman demonstrated the radiation pressure property of EM waves.

### One requires 11eV of energy to dissociate a carbon monoxide molecule into carbon and oxygen atoms. The minimum frequency of the appropriate electromagnetic radiation to achieve the dissociation lies ina) visible regionb) infrared regionc) ultraviolet regiond) microwave region

c) ultraviolet region

### Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current?

The phenomenon called Joule's law of heating is used to determine the ampere for an alternating current. According to Joule's law of heating in a one-ohm resistance, AC is the current produced in a...

### A multirange current meter can be constructed by using a galvanometer circuit shown in the figure. We want a current meter that can measure 10 mA, 100 mA, and 1 A using a galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find S1, S2, and S3 that have to be used.

I1 is measured as = 10 mA = IGG = (I1 – IG)(S1 + S2 + S3) I2 is measured as = 100 mA = IG(G+S1)=(I2-IG)(S2-S3) I3 is measured as = 1 A = IG(G+S1+S2)=(I3-IG)(S3) S1 = 1 Ω S2 = 0.1 Ω S3 = 0.01...

### Consider a circular current-carrying loop of radius R in the x-y plane with centre at the origin. Consider the line integrala) show thatmonotonically increases with L b) use an appropriate Amperian loop to thatwhere I is the current in the wire c) verify directly the above result d) suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about

a) A circular current-carrying loop's magnetic field is given as $$\Im (L)=\int_{-L}^{+L}{Bdl}=2Bl$$ It is a L function that increases monotonically. b) The Amperian loop is defined as follows:...

### An electron enters with a velocity v = v0i into a cubical region in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in the plane parallel to the x-y plane. Suggest a configuration of fields E and B that can lead to it.

The spiral route is formed by the fields E and B in their current configuration.

### A current-carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z, and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin.

The quarter's vector sum of the magnetic field at the origin is given as $${{\vec{B}}_{net}}=\frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)(\widehat{i}+\widehat{j}+\widehat{k})$$

### Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.

The time period of the radio frequency is halved when the frequency is doubled, resulting in a half revolution of the charges.

### Two identical current-carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C, a)b) the value ofc) there may be a point on C where B and dl are perpendicular d) B vanishes everywhere on C

b) the value of $$\oint\limits_{c}{B.dl$$ is independent of sense of C c) there may be a point on C where B and dl are perpendicular

### The gyro-magnetic ratio of an electron in an H-atom, according to Bohr model is a) independent of which orbit it is in b) negative c) positive d) increases with the quantum number n

a) independent of which orbit it is in b) negative

### In a cyclotron, a charged particle a) undergoes acceleration all the time b) speeds up between the dees because of the magnetic field c) speeds up in a dee d) slows down within a dee and speeds up between dees

a) undergoes acceleration all the time

### An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true? a) the electron will be accelerated along the axis b) the electron path will be circular about the axis c) the electron will experience a force at 45o to the axis and hence execute a helical path d) the electron will continue to move with uniform velocity along the axis of the solenoid

d) the electron will continue to move with uniform velocity along the axis of the solenoid

### A current circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the lop with x > 0 is now bent so that it now lies in the y-z plane. a) the magnitude of magnetic moment now diminishes b) the magnetic moment does not change c) the magnitude of B at (0,0,z),z >> R increases d) the magnitude of B at (0,0,z),z >> R is unchanged

a) the magnitude of magnetic moment now diminishes

### Two charged particles traverse identical helical paths in an opposite sense in a uniform magnetic field a) they have equal z-components of momenta b) they must have equal charges c) they necessarily represent a particle-antiparticle pair d) the charge to mass ratio satisfy: (e/m)1 + (e/m)2 = 0

d) the charge to mass ratio satisfy: (e/m)1 + (e/m)2 = 0

### Three identical bar magnets are riveted together at the centre in the same plane as shown in the figure. This system is placed at rest in a slowly varying magnetic field. It is found that the system of magnets does not show any motion. The north-south poles of one magnet is shown in the figure. Determine the poles of the remaining two.

As the system is in equilibrium, the net torque and net force will be equal to zero.

### A permanent magnet in the shape of a thin cylinder of length 10 cm has M = 106 A/m. Calculate the magnetisation current Im.

Intensity = 106 A/m l = 0.1 m M = IM/l IM = Ml = 105 A

### The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of 11.3o with the axis of the earth. At Mumbai, declination is nearly zero. Then, a) the declination varies between 11.3o W to 11.3o E b) the least declination is 0o c) the plane defined by dipole axis and the earth axis passes through Greenwich d) declination average over the earth must be always negative

a) The declination ranges from 11.3 degrees West to 11.3 degrees East.

### A metallic ring of mass m and radius l (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of the magnetic field is Bz = Bo (1+λ z). If R is the resistance of the ring and if the ring falls with a velocity v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B, λ and acceleration due to gravity g.

v = mgR/B02π2λ2l4

### A circular coil expands radially in a region of the magnetic field and no electromotive force is produced in the coil. This can be because (a) the magnetic field is constant. (b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. (d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.

(b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is...