# Physics 2015-2016 HSC Science (General) 12th Board Exam Question Paper Solution

Physics
Date & Time: 24th February 2016, 11:00 am
Duration: 3h

notes

Section I
[12] 1 | Attempt any six
[2] 1.1

In U. C. M (Uniform Circular Motion), prove the relation vec v = vec w xx vec r, where symbols have their usual meanings.

Concept: Uniform Circular Motion
Chapter: [0.01] Circular Motion
[2] 1.2

Derive an expression for critical velocity of a satellite revolving around the earth in a circular orbit.

Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth
Chapter: [0.02] Gravitation
[2] 1.3

Obtain an expression for total kinetic energy of a rolling body in the form

1/2 (MV^2)[1+K^2/R^2]

Concept: Definition of M.I., K.E. of Rotating Body
Chapter: [0.03] Angular Momentum
[2] 1.4

Define emissive power and coefficient of emmision of a body.

Concept: Heat and Temperature
Chapter: [0.09] Kinetic Theory of Gases and Radiation
[2] 1.5

A coin kept at a distance of 5cm from the centre of a turntable of radius 1.5m just begins to slip when the turntable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the turntable.

[g = 9.8 m/s2]

Concept: Centrifugal Forces
Chapter: [0.01] Circular Motion
[2] 1.6

The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of lengths of their air columns

Concept: Study of Vibrations of Air Columns
Chapter: [0.06] Superposition of Waves [0.08] Stationary Waves
[2] 1.7

A particle performing linear S.H.M. has a period of 6.28 seconds and a pathlength of 20 cm. What is the velocity when its displacement is 6 cm from mean position?

Concept: Differential Equation of Linear S.H.M.
Chapter: [0.04] Oscillations [0.05] Oscillations
[2] 1.8

The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.

Concept: Surface Tension
Chapter: [0.02] Mechanical Properties of Fluids [0.06] Surface Tension
[7] 2 | Select and write the most appropriate answer from the given alternatives for each sub-question :
[1] 2.1

A particle rotates in U.C.M. with tangential velocity V along a horizontal circle of diameter ‘D' . Total angular displacement of the particle in time 't' is..........

vt

(v/D)-t

vt/2D

2vt/D

Concept: Uniform Circular Motion
Chapter: [0.01] Circular Motion
[1] 2.2

Two springs of force constants K1 and K2 (K1> K2) are stretched by same force. If W1 and W2 be the work done stretching the springs then......

W1=W2

W1<W2

W1>W2

W1=W2=0

Concept: Elastic Energy
Chapter: [0.05] Elasticity
[1] 2.3

A and B are two steel wires and the radius of A is twice that of B. If they are stretched by the same load, then the stress on B is .....

four times that of A.

two times that of A.

three times that of A.

same as that of A.

Concept: Behaviour of Metal Wire Under Increasing Load
Chapter: [0.05] Elasticity
[1] 2.4

If sound waves are reflected from surface of denser medium, there is phase change of.......

π/4  rad

π/2 rad

Concept: Forced Oscillations and Resonance
Chapter: [0.08] Stationary Waves
[1] 2.5

A sonometer wire vibrates with frequency n1 in air under suitable load of specific gravity of . When the load is immersed in water, the frequency of vibration of wire n2 will be .........

n_1sqrt((sigma+1)/sigma)

n_1sqrt((sigma-1)/sigma)

n_1sqrt(sigma/(sigma+1))

n_1sqrt(sigma/(sigma-1))

Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth
Chapter: [0.02] Gravitation
[1] 2.6

For polyatomic molecules having 'f' vibrational modes, the ratio of two specific heats,Cp/Cv  is..........

(1+f)/(2+f)

(2+f)/(3+f)

(4+f)/(3+f)

(5+f)/(4+f)

Concept: Law of Equipartition of Energy
Chapter: [0.03] Kinetic Theory of Gases and Radiation [0.09] Kinetic Theory of Gases and Radiation
[1] 2.7

A body of moment of inertia 5 kgm2 rotating with an angular velocity 6 rad/s has the same kinetic energy as a mass of 20 kg moving with a velocity of ......

5 m/s

4 m/s

3 m/s

2 m/s

Concept: Physical Significance of M.I (Moment of Inertia)
Chapter: [0.03] Angular Momentum
[7] 3 | Attempt any one of following :
[7] 3.1

Define linear S.H.M.

Concept: Differential Equation of Linear S.H.M.
Chapter: [0.04] Oscillations [0.05] Oscillations

Show that S.H.M. is a projection of  U.C.M. on any diameter

Concept: Linear Simple Harmonic Motion (S.H.M.)
Chapter: [0.05] Oscillations

A metal sphere cools at the rate of 4°C / min. when its temperature is 50°C. Find its rate of cooling at 45°C if the temperature of surroundings is 25°C.

Concept: Heat and Temperature
Chapter: [0.09] Kinetic Theory of Gases and Radiation
OR
[7] 3.2

Explain analytically how the stationary waves are formed

Concept: Formation of Stationary Waves on String
Chapter: [0.08] Stationary Waves

Hence show that the distance between node and adjacent antinode is λ/4

Concept: Formation of Stationary Waves on String
Chapter: [0.08] Stationary Waves

A set of 48 tuning forks is arranged in a series of descending frequencies such that each fork gives 4 beats per second with preceding one. The frequency of first fork is 1.5 times the frequency of the last fork, find the frequency of the first and 42nd tuning fork

Concept: Formation of Beats
Chapter: [0.07] Wave Motion
[9] 4 | Attempt any THREE
[3] 4.1

What is the decrease in weight of a body of mass 600kg when it is taken in a mine of depth 5000m?

[ Radius of earth = 6400km, g = 9.8 m/s2 ]

Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth
Chapter: [0.02] Gravitation
[3] 4.2
[1] 4.2.1

State the theorem of parallel axes about moment of inertia.

Concept: Physical Significance of M.I (Moment of Inertia)
Chapter: [0.03] Angular Momentum
[2] 4.2.2

Prove the theorem of parallel axes about moment of inertia

Concept: Theorems of Perpendicular and Parallel Axes
Chapter: [0.01] Rotational Dynamics [0.03] Angular Momentum
[3] 4.3

Derive Laplace’s law for spherical membrane of bubble due to surface tension.

Concept: Surface Tension
Chapter: [0.02] Mechanical Properties of Fluids [0.06] Surface Tension
[3] 4.4

A steel wire having cross sectional area 1.5 mm2 when stretched by a load produces a lateral strain 1.5 x 10-5. Calculate the mass attached to the wire.

(Ysteel = 2 x 1011 N/m2, Poisson’s ratio σ = 0.291,g = 9.8 m/s2)

Concept: Definition of Stress and Strain
Chapter: [0.05] Elasticity
Section II
[12] 5 | Attempt any SIX
[2] 5.1

What is 'diffraction of light'

Concept: Fraunhofer Diffraction Due to a Single Slit
Chapter: [0.11] Interference and Diffraction

Explain two types of diffraction of light.

Concept: Fraunhofer Diffraction Due to a Single Slit
Chapter: [0.11] Interference and Diffraction
[2] 5.2

Draw a neat labelled diagram for the construction of 'cyclotron'

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
Chapter: [0.14] Magnetic Effects of Electric Current
[2] 5.3

Distinguish between ‘paramagnetic’ and ‘ferromagnetic’ substances.

Concept: Magnetic Properties of Materials
Chapter: [0.11] Magnetic Materials [0.15] Magnetism
[2] 5.4

Write a short note on surface wave propagation of electromagnetic waves.

Concept: Propagation of Electromagnetic Waves
Chapter: [0.2] Communication Systems
[2] 5.5

The combined resistance of a galvanometer of resistance 500Ω and its shunt is 21Ω. Calculate the value of shunt.

Concept: Moving Coil Galvanometer
Chapter: [0.14] Magnetic Effects of Electric Current
[2] 5.6

The susceptibility of magnesium at 200 K is 1.8 x 10-5. At what temperature will the susceptibility decrease by 6 x 10-6?

Concept: Magnetic Properties of Materials
Chapter: [0.11] Magnetic Materials [0.15] Magnetism
[2] 5.7

The co-efficient of mutual induction between primary and secondary coil is 2H. Calculate induced e.m.f. if current of 4A is cut off in 2.5 x 10-4 seconds

Concept: Inductance - Mutual Inductance
Chapter: [0.12] Electromagnetic Induction [0.16] Electromagnetic Inductions
[2] 5.8

The decay constant of radioactive substance is 4.33 x 10-4 per year. Calculate its half life period.

Chapter: [0.15] Structure of Atoms and Nuclei [0.18] Atoms, Molecules and Nuclei
[7] 6 | Select and write the most appropriate answer from the given alternatives for each sub-question :
[7] 6.1

If the polarising angle for a given medium is 60°, then the refractive index of the medium is.................

1/sqrt3

sqrt(3/2)

1

sqrt3

Concept: Polarisation
Chapter: [0.1] Wave Theory of Light
[1] 6.2

The resolving power of a telescope depends upon the...............

length of the telescope

focal length of an objective

diameter of an objective

focal length of an eyepiece

Concept: Resolving Power of a Microscope and Telescope
Chapter: [0.11] Interference and Diffraction
[1] 6.3

Electric intensity due to a charged sphere at a point outside the sphere decreases with...................

increase in charge on sphere.

increase in dielectric constant.

decrease in the distance from the centre of sphere.

decrease in square of distance from the centre of sphere.

Concept: Dielectrics and Polarisation
Chapter: [0.12] Electrostatics
[1] 6.4

In potentiometer experiment, if l1 is the balancing length for e.m.f. of cell of internal resistance r and l2 is the balancing length for its terminal potential difference when shunted with resistance R then :

l_1=l_2((R+r)/R)

l_1=l_2((R)/(R+r))

l_1=l_2((R)/(R-r))

l_1=l_2((R-r)/R)

Concept: Metre Bridge
Chapter: [0.13] Current Electricity
[1] 6.5

The energy of photon of wavelength X is_____ .

[h = Planck’s constant, c = speed of light in vacuum]

hcλ

(hλ)/c

λ/(hc)

(hc)/λ

Concept: Einstein’s Equation - Particle Nature of Light
Chapter: [0.17] Electrons and Photons
[1] 6.6

Which logic gate corresponds to the truth table given below?

 A B Y 0 0 I 0 1 0 1 0 0 1 1 0

AND

NOR

OR

NAND

Concept: Digital Electronics and Logic Gates
Chapter: [0.19] Semiconductors
[1] 6.7

The process of superimposing a low frequency signal on a high frequency wave is_______ .

detection

mixing

modulation

attenuation

Concept: Modulation and Its Necessity
Chapter: [0.2] Communication Systems
[7] 7 | Attempt any one of the following :
[7] 7.1

State the principle on  which transformer works.

Concept: Transformers
Chapter: [0.12] Electromagnetic Induction [0.16] Electromagnetic Inductions

Explain transformer working with construction.

Concept: Transformers
Chapter: [0.12] Electromagnetic Induction [0.16] Electromagnetic Inductions

Derive an expression for ratio of e.m.f.s and currents in terms of number of turns in primary and secondary coil.

Concept: Transformers
Chapter: [0.12] Electromagnetic Induction [0.16] Electromagnetic Inductions

A conductor of any shape, having area 40 cm2 placed in air is uniformly charged with a charge 0* 2µC. Determine the electric intensity at a point just outside its surface. Also, find the mechanical force per unit area of the charged conductor.

[∈0=8.85x10-12 S.I. units]

Concept: Mechanical Force on Unit Area of a Charged Conductor
Chapter: [0.12] Electrostatics
OR
[7] 7.2

With the help of a neat labelled diagram, describe the Geiger- Marsden experiment

Concept: Alpha-particle Scattering and Rutherford’S Nuclear Model of Atom
Chapter: [0.18] Atoms, Molecules and Nuclei

What is mass defect?

Concept: Mass-Energy Relation and Mass Defect
Chapter: [0.18] Atoms, Molecules and Nuclei

The photoelectric work function for a metal surface is 2.3 eV. If the light of wavelength 6800A is incident on the surface of metal, find threshold frequency and incident frequency. Will there be an emission of photoelectrons or not?

[Velocity of light c = 3 x 108 m/s,

Planck’s constant, h = 6.63 * 10-34 Js ]

Concept: Photoelectric Effect - Hertz’S Observations
Chapter: [0.17] Electrons and Photons
[9] 8 | Attempt any three :
[3] 8.1

Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is 1.5 and the frequency of light is 3.5 x 1014 Hz, find the wave number of light in glass.

[Velocity of light in air c = 3 x 108 m/s]

Concept: Reflection and Refraction of Plane Wave at a Plane Surface Using Wave Fronts
Chapter: [0.1] Wave Theory of Light
[3] 8.2

In biprism experiment, 10th dark band is observed at 2.09 mm from the central bright point on the screen with red light of wavelength 6400 A. By how much will fringe width change if blue light of wavelength 4800A is used with the same setting?

Concept: Measurement of Wavelength by Biprism Experiment
Chapter: [0.11] Interference and Diffraction
[3] 8.3

Describe Kelvin’s method to determine the resistance of the galvanometer by using a meter bridge.

Concept: Galvanometer
Chapter: [0.09] Current Electricity
[3] 8.4

Explain the elementary idea of an oscillator with the help of block diagram

Concept: Oscillators
Chapter: [0.19] Semiconductors

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