HSC Physics SAMPLE PAPER-3 – Maharashtra Board Solutions

Section A

HSC Physics SAMPLE PAPER-3

Select and write the correct answers to the following questions:

(i) The coefficient of absorption and coefficient of transmission are 0.50 and 0.25 respectively. If 200 calories of radiant heat is incident on the surface of the body, the quantity of heat reflected will be:
(a)

(b)

(c)

(d)

(ii) If and , then the value of tr is:
(a) 0.02
(b) 0.04
(c) 0.4
(d) 0.2

(iii) For an isothermal process, which of the following quantities are non zero?
(a) and
(b) Q and W
(c) and
(d) and

(iv) A gas in a closed container in heated with of energy, causing the lid of the container to rise with of force. What is the total change in energy of the system?
(a)
(b)
(c)
(d)

(v) A standing wave is produced on a string fixed at one end with the other end free. The length of the string:

(a) Must be an odd integral multiple of

(b) Must be an odd integral multiple of

(d) Must be an even integral multiple of

(vi) When the balance point is obtained in the potentiometer, a current is drawn from:

(a) Both the cells and auxiliary battery

(b) Cell only

(d) Neither cell nor auxiliary battery

(vii) A charged particle is in motion having initial velocity when it enter into a region of uniform magnetic field perpendicular to . Because of the magnetic force the kinetic energy of the particle will:
(a) Remain unchanged
(b) Get reduced
(c) Increase
(d) Be reduced to zero

(viii) In a series LCR circuit the phase difference between the voltage and the current is 450 . Then the power factor will be:
(a) 0.607
(b) 0.707
(c) 0.808
(d) 1

(ix) Light of frequency 1.9 times the threshold frequency is incident on a photo sensitive material. If the frequency is halved and intensity is doubled, the photo current becomes.
(a) doubled
(b) quadrupled
(c) halved
(d) zero

(x) The SI units and dimensions of Reynolds number respectively are ….

33. Answer the following questions:

(i) Do we need a banked road for a two-wheeler? Explain.

(ii) What is an incompressible fluid?

(iii) A gas contained in a cylinder surrounded by a thick layer of insulating material is quickly compressed. Has there been a transfer of heat?

(iv) What are primary and secondary sources of light?

(v) The dipole moment of a water molecule is . A sample of water contains molecule, whose dipole moments are all oriented in an electric field of strength . Calculate the work to be done to rotate the dipoles from their initial orientation to one in which all the dipoles are perpendicular to the field .

(vi) What do you mean by electromagnetic induction?

(vii) What is photoelectric effect?

(viii) State the principal of solar cell?

34. Section B

35. Attempt any Eight of the following questions:

State (i) Stefan’s Boltzmann law of radiation (ii) Kirchhoff’s law of heat radiation.
At what distance from the mean position is the speed of a particle performing S.H.M. half its maximum speed. Given path length of S.H.M. .
Why are multiple colours observed over a thin film of oil floating on water?
The safest way to protect yourself from lightening is to be inside a car. Justify.
A voltmeter has a resistance . What will be its reading. when it is connected across a cell of emf having internal resistance ?
A very long straight wire carries a current 5.2 A. What is the magnitude of the magnetic field at a distance from the wire?

When a plate of magnetic material of size (length, breadth and thickness resp) is located is magnetic moment of . Find magnetization.
State the difficulties faced by Rutherford atomic model?
If the effective current is a 50 cycle circuit is , what is the peak value of current? What is the current sec. after if was zero?
Two soap bubbles have radii in the ratio . What is the ratio of work done to blow these bubbles.
A horizontal wire long extending from east to west is falling with a velocity of normal to the Earth’s magnetic field of . What is the value of induced emf in the wire?
State characteristics of stationary waves?

36. Section C

37. Attempt any Eight of the following questions:

Prove the theorem of perpendicular axes about moment of inertia
Derive an expression of excess pressure inside a liquid drop.
State and prove Kirchhoff’s law of heat radiation.
A solar-cooker and a pressure-cooker both are used to cook food. Treating them as thermodynamic systems, discuss the similarities and difference between them.
State the laws of simple pendulum.
Two wires of the same material and same cross-section are stretched on a sonometer. One wire is loaded with 1.5 and another is loaded with . The vibrating length of first wire is and its fundamental frequency of vibration is the same as that of the second wire. Calculate vibrating length of the other wire.
A double-slit arrangement produces interference fringes for sodium light ) that are apart What is the angular fringe separation if the entire arrangement is immersed in water ?
A voltmeter has a resistance of What will be its reading when it is connected across a cell of emf and internal resistance ?
Current of equal magnitude flows through two long parallel wires having separation of . If the force per unit length on each of the wires in . what must be I?
Define magnetization. State its formula, SI unit and dimension. What is magnetic susceptibility of a medium?
A capacitor is connected to a source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what will happen to the capacitive reactance and the current
Explain the inverse linear dependence of stopping potential on the incident wavelength in a photoelectric effect experiment.

38. Section D

39. Attempt any Three of the following questions:

Derive an expression that relates angular momentum with the angular velocity of a rigid body
Explain the principle of operation of a photodiode.
In a parallel plate capacitor with air between the plates, each plate has an area of and the separation between the plates is .

(i) Calculate the capacitance of the capacitor.

(ii) If this capacitor is connected to supply, what would be the charge on each plate? (iii) How would charge on the plates be affected if a 2 thick mica sheet of is inserted between the plates while the voltage supply remains connected?

In a Faraday disc dynamo, a metal disc of radius rotates with an angular velocity about an axis perpendicular to the plane of the disc and passing through its centre. The disc is placed in a magnetic field acting perpendicular to the plane of the disc. Determine the induced emf between the rim and the axis of the disc.
Determine the series limit of Balmer, Paschen and Pfund series, given the limit for Lyman series is .

40. Answer Key

41. Section A

(i) (c)

(ii) (c) 0.4

(iii) (b) Q and W

(iv) (b)

(v) (a) Must be an odd integral multiple of

(vi) (d) Neither cell nor auxiliary battery

(vii) (a) Remain unchanged

(viii) (b) 0.707

(ix) (d) Zero

(x) (c) No unit, [
2. (i) When a two-wheeler takes a turn along an unbanked road, the force of friction provides the centripetal force. The two-wheeler leans inward to counteract a torque that tends to topple it outward. Firstly, friction cannot be relied upon to provide the necessary centripetal force on all road conditions. Secondly, the friction results in the wear and tear of the tyres. On a banked road at a turn, any vehicle can negotiate the turn without depending on friction and without straining the tyres.
(ii) An incompressible fluid is one which does not undergo a change in volume for a large range of pressures. Thus, it density has a constant value throughout the fluid. In most cases, all liquids are incompressible.

(iii) No. There is no transfer of heat energy. as the cylindrical vessel is surrounding by an insulating material, which doesn’t allow heat transfer.

(iv) Primary sources of light: The sources that emit light on their own are called primary sources. This emission of light may be due to:

(a) The high temperature of the source, e.g, the Sun, the stars, objects heated to high temperature, a flame, etc.

(b) The effect of current being passed through the source, e.g, tubelight, TV, etc.

Secondary sources of light: Some sources are not self-luminous, i.e. they do not emit light on their own, but reflect or scatter the light incident on them. Such sources of light are called secondary sources, e.g., the moon, the planets, objects such as humans, animals, plants, etc. These objects are visible due to reflected light.
Many of the sources that we see around are secondary sources and most of them are extended sources.

(v)

This is the required angular fringe separation.

(vi) The phenomenon of production of emf in a conductor or circuit by a changing magnetic flux through the circuits is called electromagnetic induction.

(vii) The phenomenon of emission of electrons from a metal surface when electromagnetic radiation of appropriate frequency is incident on it is known as photoelectric effect.

(viii) A solar cell is an unbiased pn-junction that converts the energy of sunlight directly into electricity with a high conversion efficiency.

Principle: A solar cell works on the photovoltaic effect in which an emf is produced between the two layers of a pn-junction as a result of irradiation.

42. Section B

(i) Stefan’s Boltzmann law of radiation: The rate of emission of radiant energy per unit area or the power radiated per unit area of a perfect black body is directly proportional to the fourth power of its absolute temperature.

(ii) Kirchhoff’s law of heat radiation: At a given temperature the ratio to emissive power to coefficient of absorption of a body is equal to the emissive power of a perfect black body at the same temp. for all wavelengths.

i.e.

Given:

Since

This gives the required displacement.

Interference due to a thin film: The brilliant colours of soap bubbles and thin films on the surface of water are due to the interference of light waves reflected from the upper and lower surfaces of the film. The two rays have a path difference which depends on the point on the film that is being viewed. This is shown in above figure.

The incident wave gets partially reflected from upper surface as shown by ray . The rest of the light gets refracted and travels along . At it again partially reflected and travels along . At it refracts into air and travels CF. The parallel rays and have a phase difference due to their different path lengths in different media. As can be seen from the figure, the phase difference depends on the angle of incidence , i.e. the angle of incidence at the top surface which is the angle of viewing and also on the wavelength of the light as the refractive index of the material of the thin film depends on it. The two waves propagating along and interfere producing maxima and minima for different colours at different angles of viewing. One sees different colours when the film is viewed at different angles.

As the reflection is from the denser boundary, there is an additional phase difference of radians (or an additional path difference ). This should be taken into account for mathematical analysis.

There is a danger of lightning strikes during a thunderstorm. Because trees are taller than people and therefore closer to the clouds above, they are more likely to get hit by lightnings. Similarly, a person standing in an open ground is the tallest object and more likely to get hit by lightning. But a car with a metal body is an almost idea Faraday cage. When a car is struck by lightning, the charge flows on the outside surface of the car to the ground but the electric field inside remains zero. This leaves the passengers inside unharmed.
Given:

The voltmeter reading.

Given:

The magnetic induction,

Given,

(i) According to Rutherford, the electrons revolve in circular orbits around the atomic nucleus. The circular motion is an accelerated motion. According to the classical electromagnetic theory, an accelerated charge continuously radiates energy. Therefore, an electron during its orbital motion should go on radiating energy. Due to the loss of energy, the radius of its orbit should go on decreasing. Therefore, the electron should move along a spiral path and finally fall into the nucleus in a very short time, of the order of in the case of a hydrogen atom. Thus, the atom should be unstable. We exist because atoms are stable.

(ii) If the electron moves along such a spiral path, the radius of its orbit would continuously decrease. As a result, the speed and frequency of revolution of the electron would go on increasing. The electron, therefore, would emit radiation of continuously changing frequency and hence give rise to a continuous spectrum. However, the atomic spectrum is a line spectrum.
11. Given:

The peak value of the current,

12.

Given: The magnitude of the induced emf,

Stationary wave: When two, identical, progressive waves of equal amplitudes and equal wavelengths and travelling in a similar medium, along the similar straight line but in opposite directions, interfere and then the wave formed is called a standing wave or a stationary wave.

43. Characteristics of stationary waves:

(i) Stationary waves are produced by the interference of two identical progressive waves travelling in opposite directions, under certain conditions.

(ii) The overall appearance of a standing wave is of alternate intensity maximum (displacement antinode) and minimum (displacement node).

(iii) The distance between adjacent nodes (or antinodes) is .

(iv) The distance between successive node and antinode is .

(v) There is no progressive change of phase from particle to particle. All the particles in one loop, between two adjacent nodes, vibrate in the same phase, while the particles in adjacent loops are in opposite phase.

(vi) A stationary wave does not propagate in any direction and hence does not transport energy through the medium.

44. Section C

15.

Let and be two perpendicular axes in the plane to the lamina and an axis perpendicular to the its plane. Consider an infinitesimal mass element ‘ ‘ of the lamina at the point .

M.I of the lamina about -axis

The element is at perpendicular distance and from the and axes respectively. Hence M.I. about area are

from figure,

Integrating wrt dm on both cld

This proves the theorem of perpendicular axes.

Consider a liquid drop of radius and surface tension .

Due to surface tension, the molecules on the surface film experience the net force in the inward direction normal to the surface. Therefore, there is more pressure inside than outside.

Let be the pressure inside the liquid drop and be the pressure outside the drop.

Therefore, excess of pressure inside the liquid drop is

Due to excess pressure inside the liquid drop the free surface on the drop will experience the net force in outward direction due to which the drop will expand.

Let the free surface displace by under isothermal conditions.

Therefore, excess of pressure does the work in displacing the surface and that work will be stored in the form of potential energy

The work done by an excess of pressure in displacing the surface is

Increase in the potential energy is,

increase in area of the free surface

From equations ( 1 ) and (2),

The above expression gives us the pressure inside a liquid drop.

Consider an ordinary body and perfectly black body of the same dimension suspended in a uniform temperature enclosure as shown in the figure.

At thermal equilibrium, both the bodies will have the same temperature as that of the enclosure.

Let emissive power of ordinary body

emissive power of perfectly black body

coefficient of absorption of

emissivity of

radiant energy incident per unit time per unit area on each body

Quantity of heat absorbed per unit area per unit time by body .

Quantity of heat energy emitted per unit area per unit time by body .

Since there is no change in temperature

Quantity of heat absorbed per unit area per unit time by a perfectly black body.

The radiant heat energy emitted per unit time per unit area by a perfectly black body.

Since there is no change in temperature,

From equations

(1) and (2).

45. Solar cooker:

Solar cooker was invented by Horace Benedict de saussure in 1767.
Solar cooker is device used to cook food by using no fuel, instead of sunlight.
Solar cookers use a parabolic reflector to collect the rays of the sun and focus them at the cooker to heat it and cook the food in the cooker.
Today the solar cookers are a little bit expensive than pressure cookers.
Big solar cookers can be used to make food for people on a larger scale.

46. Pressure cooker:

Pressure cooker was invented by Denis papin.
Pressure cookers are the most common cookers used in our houses and can be found in every house.
Pressure cookers require water to convert it into steam for raising the internal temperature and pressure that permits quick cooking.
Pressure cooker are cheaper than solar cookers.
Pressure cookers requires a fuel for heating the liquid inside them.

The period of a simple pendulum at a given place is

where is the length of the simple pendulum and is the acceleration due to gravity at the place. From the above expression, the laws of a simple pendulum are as follows:

Law of length: The period of a simple pendulum at a given place ( constant) is directly proportional to the square root of its length.

Law of acceleration due to gravity: The period of a simple pendulum of a given length ( constant) is inversely proportional to the square root of the acceleration due to gravity.

Law of mass: The period of a simple pendulum does not depend on the mass of material of the bob of the pendulum.
Law of isochronism: The period of a simple pendulum does not depend on the amplitude of oscillations, provided that the amplitude is small.

Given: ,

But

The vibrating length of the second wire is .

Given:

In the first approximation,

For given and ,

From equations (1), (2) and (3), we get

This is the required angular fringe separation.

Given:

To find: Reading of voltmeter

Formula:

Calculation: Current through the circuit is given by

From formula,

The reading on the voltmeter is .

Given:

Magnetization: The net magnetic moment per unit volume of a material is called the magnetization.

Formula:

Sl unit: ampere per meter

Dimensions:

Magnetic susceptibility: The magnetic susceptibility of a medium is a dimensionless quantify which signifies the contribution made by the medium when subjected to a magnetic field to the magnetic induction inside the medium.

Given: The capacitive reactance

If the frequency is doubled, the capacitive reactance will be halved and the current will be doubled.

We have , where is the stopping potential, is the magnitude of the charge on the electron, his Planck’s constant is the speed of light in free space, is the wavelength of the electromagnetic radiation incident on a metal surface and is the work function for the metal, and are constants, is constant for a particular metal.

Hence, it follows that as increases, increases.

The plot of verses is linear. This is because the energy associated with a quantum of radiation (photon) is directly proportional to the frequency of the radiation and hence inversely proportional to the wavelength of radiation.

47. Section D

Consider a rigid body rotating with a constant angular velocity about an axis through the point and perpendicular to the plane of the figure. All the particles of the body perform uniform circular motion about the axis of rotation with the same angular velocity . Suppose that the body consists of particles of masses situated at perpendicular distances . , respectively from the axis of rotation.

The particle of mass revolves along a circle of radius with a linear velocity of magnitude . The magnitude of the linear momentum of the particle is

The angular momentum of the particle about the axis of rotation is by definition,

where is the smaller of the two angles between

and .

In this case,

Similarly, , etc.

The angular momentum of the body about the given axis is

the given axis.

In vector form,

Thus, angular momentum moment of inertia

angular velocity.

Construction: A photodiode consists of an n-type silicon substrate with a metal electrode back contact. A thin -type layer is grown over the -type substrate by diffusing a suitable acceptor dopant.

The area of the player defines the photodiode active area. An Ohmic contact pad is deposited on the active area. The rest of the active area is left open with a protective anti-reflective coating of silicon nitride to minimize the loss of photons. The non-active area is covered with an insulating opaque coating.

Depending on the required spectral sensitivity, i.e. the operating wavelength range, typical photodiode materials are silicon, germanium, indium gallium arsenide phosphide (InGaAsP) and indium gallium arsenide (InGaAs), of which silicon is the cheapest while the last two are expensive.

Working: The band gap energy of silicon is at room temperature. Thus, photons or particles with energies greater than or equal to , which corresponds to , can transfer electrons from the valence band into the conduction band. A photodiode is operated in the reverse bias mode which results in a wider depletion region. When operated in the dark (zero illumination), there is a reverse saturation current due solely to the thermally generated minority charge carriers. This is called the dark current. Depending on the minority carrier concentrations, the dark current is an photodiode may range from to .

When exposed to radiation of energy (in the range near-UV to near-IR), electron-hole pairs are created in the depletion region. The electric field in the depletion
layer accelerates these photogenerated electrons and holes towards the -side and -side, respectively. constituting a photocurrent in the external circuit from the -side to the -side. Due to the photogeneration, more change carriers are available for conduction and the reverse current is increased. The photocurrent is directly proportional to the intensity of the incident light. It is independent of the reverse bias voltage.

(i) Silicon (Si): Low dark current, high speed, good sensitivity between and (best around ).

(ii) Germanium (Ge): High dark current, slow speed, good sensitivity between and (best around ).

(iii) Indium gallium arsenide phosphide (InGaAsP): Expensive low dark current, high speed, good sensitivity between and (best around 1100 run- ).

(iv) Indium gallium arsenide (InGaAs): Expensive, low dark current, high speed, good sensitivity between and (best around nm).

Given: (air), ,

(i) The capacitance of the air capacitor

(ii)

(iii) The dielectric of relative permittivity completely fills the space between the plates , so that the new capacitance is .

With the supply still connected, remains the same.

Therefore, the charge on the plates increases.

Suppose thin conducting disc of radius is rotated anticlockwise, about its axis, in a plane perpendicular to a uniform magnetic field of induction points downwards. Let the constant angular speed of the disc be .

Consider an infinitesimal element of radial thickness at a distance from the rotation axis. In one rotation, the area traced by the element is . Therefore, the time rate at which the element traces out the area is