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Physics 2012-2013 HSC Science (General) 12th Board Exam Question Paper Solution

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Physics
2012-2013 October
Marks: 70

[7]1 | Attempt Any One
[7]1.1

Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?

Concept: Periodic and Oscillatory Motions
Chapter: [4] Oscillations

A ballet dancer spins about a vertical axis at 2.5Π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m.

Concept: Physical Significance of M.I (Moment of Inertia)
Chapter: [3] Angular Momentum
[7]1.2

Discuss different modes of vibrations in an air column of a pipe open at both the ends.

Concept: Study of Vibrations of Air Columns
Chapter: [8] Stationary Waves

Draw neat labelled diagrams for modes of vibration of an air column in a pipe when it is closed at one end.

Hence derive an expression for fundamental frequency in each case.

Concept: Study of Vibrations of Air Columns
Chapter: [8] Stationary Waves

A soap bubble of radius 12 cm is blown. Surface tension of soap solution is 30 dyne/cm. Calculate the work done in blowing the soap bubble.

Concept: Capillarity and Capillary Action
Chapter: [6] Surface Tension
[9]2 | Attempt any THREE:
[3]2.1

In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass
of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a
vertical axis, calculate tension in the string (g = 9.8 m/s2)

Concept: Surface Tension
Chapter: [6] Surface Tension
[3]2.2

Discuss the behaviour of wire under increasing load.

Concept: Definition of Stress and Strain
Chapter: [5] Elasticity
[3]2.3

Derive an expression for one dimensional simple harmonic progressive wave travelling in the
direction of positive X-axis. Express it in ‘two’ different forms.

Concept: Simple Harmonic Progressive Waves,
Chapter: [7] Wave Motion
[3]2.4

The kinetic energy of nitrogen per unit mass at 300 K is 2.5 × 106 J/kg. Find the kinetic energy of 4 kg oxygen at 600 K. (Molecular weight of nitrogen = 28, Molecular weight of oxygen = 32)

Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
Chapter: [4] Oscillations
[12]3 | Attempt any SIX:
[2]3.1

A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track
if the car has uniform centripetal acceleration of Π2 m/s2.

Concept: Dynamics of Uniform Circular Motion - Centripetal Force
Chapter: [1] Circular Motion
[2]3.2

A body weighs 4.0 kg-wt on the surface of the Earth. What will be its weight on the surface of a plant whose mass is `1/8` th of the mass of the Earth and radius half `(1/2)` of that of the Earth?

Concept: Surface Tension
Chapter: [6] Surface Tension
[2]3.3

Define radius of gyration

Concept: Physical Significance of M.I (Moment of Inertia)
Chapter: [3] Angular Momentum

Explain the physical significance of radius of gyration

Concept: Physical Significance of M.I (Moment of Inertia)
Chapter: [3] Angular Momentum
[2]3.4

A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:

a) Angular frequency

b) frequency of vibration.

Concept: Simple Harmonic Motion
Chapter: [4] Oscillations
[2]3.5

Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.

Concept: Surface Tension
Chapter: [6] Surface Tension
[2]3.6

Show graphical representation of energy distribution spectrum of perfectly black body.

Concept: Qualitative Ideas of Blackbody Radiation
Chapter: [9] Kinetic Theory of Gases and Radiation

Explain black body radiation spectrum in terms of wavelength

Concept: Qualitative Ideas of Blackbody Radiation
Chapter: [9] Kinetic Theory of Gases and Radiation
[2]3.7

‘g’ is the acceleration due to gravity on the surface of the Earth and ‘R’ is the radius of the
Earth.

Show that acceleration due to gravity at height ‘h’ above the surface of the Earth is

`gh = g (R/(R+H))^2`

Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth
Chapter: [2] Gravitation
[2]3.8

In Melde’s experiment, the number of loops on a string changes from 7 to 5 by the addition of 0.015 kgwt. Find the initial tension applied to the string.

Concept: Formation of Stationary Waves on String
Chapter: [8] Stationary Waves
[7]4 | Select and write the most appropriate answer from the given alternatives for each sub-questions:
[1]4.1

A planet is revolving around a star in a circular orbit of radius R with a period T. If the
gravitational force between the planet and the star is proportional to `R^(-3/2)` then

A) `T^2 prop R^(5/2)`

B) `T^2 prop R^((-7)/2)`

C) `T^2 prop R^(3/2)`

D) `T^2 prop R^4`

Concept: Vertical Circular Motion Due to Earth’s Gravitation
Chapter: [1] Circular Motion
[1]4.2

If ‘L’ is the angular momentum and ‘I’ is the moment of inertia of a rotating body, then `L^2/(2I)`represents its _____

(A) rotational P.E.

(B) total energy

(C) rotational K.E.

(D) translational K.E

Concept: Definition of M.I., K.E. of Rotating Body
Chapter: [3] Angular Momentum
[1]4.3

A particle executing linear S.H.M. has velocities v1 and v2 at distances x1 and x2 respectively from the mean position. The angular velocity of the particle is _______

A) `sqrt((x_1^2 - x_2^2)/(v_2^2 - v_1^2))`

B) `sqrt((v_2^2 - v_1^2)/(x_1^2 - x_2^2))`

C) `sqrt((x_1^2 + x_2^2)/(v_2^2 + v_1^2))`

D) `sqrt((v_2^2 + v_1^2)/(x_2^2 + x_1^2))`

Concept: Differential Equation of Linear S.H.M.
Chapter: [4] Oscillations
[1]4.4

A metal rod having coefficient of linear expansion (α) and Young’s modulus (Y) is heated to
raise the temperature by ΔΘ. The stress exerted by the rod is _______

A) `(Yα)/(ΔΘ)`

B) `(YΔΘ)/α`

C) YαΔΘ

D) `(αΔΘ)/Y`

Concept: Definition of Stress and Strain
Chapter: [5] Elasticity
[1]4.5

A big drop of radius R is formed from 1000 droplets of water. The radius of a droplet will be _______

A) 10 R

B) R/10

C) R/100

D) R/1000

Concept: Surface Tension
Chapter: [6] Surface Tension
[1]4.6

Apparent frequency of the sound heard by a listener is less than the actual frequency of sound emitted by source. In this case _______.

(A) listener moves towards source

(B) source moves towards listener

(C) listener moves away from the source.

(D) source and listener move towards each other.

Concept: Beats
Chapter: [7] Wave Motion [10] Wave Theory of Light
[1]4.7

The substance which allows heat radiations to pass through is _______.

(A) iron

(B) water vapour

(C) wood

(D) dry air

Concept: Temperature and Heat
Chapter: [9] Kinetic Theory of Gases and Radiation
[7]5 | Attempt Any One
[7]5.1

Obtain an expression for the induced e.m.f. in a coil rotating with uniform angular velocity in
uniform magnetic field. Plot a graph of variation of induced e.m.f. against phase (Θ = ωt) over one cycle.

Concept: Magnetic Properties of Materials
Chapter: [15] Magnetism

The energy density at a point in a medium of dielectric constant 6 is 26.55 × 106 J/m3. Calculate electric field intensity at that point. (ε0 = 8.85 × 10−12 SI units).

Concept: Energy Density of a Medium
Chapter: [12] Electrostatics
[7]5.2

Write notes on Nuclear fission

Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars
Chapter: [18] Atoms, Molecules and Nuclei

Write notes on Nuclear fusion

Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars
Chapter: [18] Atoms, Molecules and Nuclei

A galvanometer has a resistance of 16Ω. It shows full scale deflection, when a current of 20 mA is passed through it. The only shunt resistance available is 0.06  which is not appropriate to convert a galvanometer into an ammeter. How much resistance should be connected in series with the coil of galvanometer, so that the range of ammeter is 8 A?

Concept: Moving Coil Galvanometer
Chapter: [14] Magnetic Effects of Electric Current
[9]6 | Attempt any THREE
[3]6.1

Draw a well labelled diagram of photoelectric cell.

Concept: Particle Nature of Light
Chapter: [17] Electrons and Photons

Explain the observations made by Hertz and Lenard about the phenomenon of photoelectric
emission.

Concept: Particle Nature of Light
Chapter: [17] Electrons and Photons
[3]6.2

Explain the working of transistor as a switch.

Concept: Transistor as a Switch
Chapter: [19] Semiconductors
[3]6.3

The refractive indices of water for red and violet colours are 1.325 and 1.334 respectively.
Find the difference between the velocities of rays for these two colours in water. (c = 3 × 108 m/s)

Concept: Polarisation
Chapter: [10] Wave Theory of Light
[3]6.4

In Young’s experiment, the ratio of intensity at the maxima and minima in an interference
pattern is 36 : 9. What will be the ratio of the intensities of two interfering waves?

Concept: Interference of Light Waves and Young’S Experiment
Chapter: [11] Interference and Diffraction
[12]7 | Attempt any SIX:
[2]7.1

Explain the principle of potentiometer.

Concept: Meter Bridge
Chapter: [13] Current Electricity
[2]7.2

Define Magnetic intensity.

Concept: Magnetisation and Magnetic Intensity
Chapter: [15] Magnetism
[2]7.3

What do you mean by polar molecules and non-polar molecules? Give ‘one’ example each.

Concept: Atomic Masses and Composition of Nucleus
Chapter: [18] Atoms, Molecules and Nuclei
[2]7.4

The minimum angular separation between two stars is 4 × 10−6 rad, if telescope is used to observe them with an objective of aperture 16 cm. Find the wavelength of light used.

Concept: Wave Theory of Light
Chapter: [10] Wave Theory of Light
[2]7.5

Explain the need for modulation related to the size of antenna (aerial).

Concept: Modulation and Its Necessity
Chapter: [20] Communication Systems
[2]7.6

Four resistances 4Ω,8Ω,XΩ, and 6Ω are connected in a series so as to form Wheatstone’s
network. If the network is balanced, find the value of ‘X’.

Concept: Wheatstone Bridge
Chapter: [13] Current Electricity
[2]7.7

The magnetic susceptibility of annealed iron at saturation is 4224. Find the permeability of
annealed iron at saturation. (μ0 = 4Π × 10−7 SI unit)

Concept: Magnetic Properties of Materials
Chapter: [15] Magnetism
[7]8 | Select and write the most appropriate answer from the given alternatives for each subquestions:
[1]8.1

A ray of light passes from a vacuum to a medium of refractive index (μ). The angle of
incidence is found to be twice the angle of refraction. The angle of incidence is _______.

A) `cos^(-1)(mu/2)`

B) cos−1(μ)

C)  `2 cos^(-1) (mu/2)`

D) `2 sin^(-1) (mu/2)`

Concept: Polarisation
Chapter: [10] Wave Theory of Light
[1]8.2

The fringes produced in diffraction pattern are of _______.

(A) equal width with same intensity

(B) unequal width with varying intensity

(C) equal intensity\

(D) equal width with varying intensity

Concept: Interference of Light Waves and Young’S Experiment
Chapter: [11] Interference and Diffraction
[1]8.3

If ‘R’ is the radius of dees and ‘B’ be the magnetic field of induction in which positive charges (q) of mass (m) escape from the cyclotron, then its maximum speed (vmax) is _______.

A) `(qR)/(Bm)`

B)`(qm)/(Br)`

C) `(qBR)/m`

D) `m/(qBR)`

Concept: Electromagnetic Induction
Chapter: [16] Electromagnetic Inductions
[1]8.4

The number of photoelectrons emitted _______.

(A) varies inversely with frequency

(B) varies directly with frequency

(C) varies inversely with intensity

(D) varies directly with intensity

Concept: Particle Nature of Light
Chapter: [17] Electrons and Photons
[1]8.5

The width of depletion region of p-n junction diode is _______.

(A) 0.5 nm to 1 nm

(B) 5 nm to 10 nm

(C) 50 nm to 500 nm

(D) 500 nm to 1000 nm

 

Concept: Special Purpose P-n Junction Diodes
Chapter: [19] Semiconductors
[1]8.6

Any device that converts one form of energy into another is termed as ______.

(A) amplifier

(B) transducer

(C) receiver

(D) demodulator

Concept: Elements of a Communication System
Chapter: [20] Communication Systems
[1]8.7

A transformer converts 240 V AC to 60 V AC. The secondary has 75 turns. The number of turns in primary are _______.

(A) 600

(B) 500

(C) 400

(D) 300

 

Concept: Transformers
Chapter: [16] Electromagnetic Inductions

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