Date & Time: 26th February 2015, 11:00 am

Duration: 3h

The period of a conical pendulum in terms of its length (l), semi-vertical angle (θ) and acceleration due to gravity (g) is:

`1/(2pi)sqrt((l costheta)/g)`

`1/(2pi)sqrt((l sintheta)/g)`

`4pisqrt((lcostheta)/(4g))`

`4pisqrt((l tantheta)/g)`

Chapter: [0.04] Oscillations

The kinetic energy of a rotating body depends upon................

- distribution of mass only.
- angular speed only.
- distribution of mass and angular speed.
- angular acceleration only.

Chapter: [0.03] Angular Momentum

If the metal bob of a simple pendulum is replaced by a wooden bob of the same size, then its time period will.....................

- increase
- remain same
- decrease
- first increase and then decrease.

Chapter: [0.04] Oscillations

The graph between applied force and change in the length of wire within elastic limit is a.......................

- straight line with positive slope.
- straight line with negative slope.
- curve with positive slope.
- curve with negative slope.

Chapter: [0.05] Elasticity

When longitudinal wave is incident at the boundary of denser medium, then............................

- compression reflects as a compression.
- compression reflects as a rarefaction.
- rarefaction reflects as a compression.
- longitudinal wave reflects as transverse wave.

Chapter: [0.07] Wave Motion

The dimensions of universal gravitational constant are........................

a. [L^{1}M^{0}T^{0}]

b. [L^{2}M^{1}T^{0}]

c. [L^{-1}M^{1}T^{-2}]

d. [L^{3}M^{-1}T^{-2}]

Chapter: [0.02] Gravitation

Two copper spheres of radii 6 cm and 12 cm respectively are suspended in an evacuated enclosure. Each of them are at a temperature 15°C above the surroundings. The ratio of their rate of loss of heat is.................

- 2:1
- 1:4
- 1:8
- 8:1

Chapter: [0.09] Kinetic Theory of Gases and Radiation

In circular motion, assuming `bar v = bar w xx bar r` , obtain an expression for the resultant acceleration of a particle in terms of tangential and radial component.

Chapter: [0.01] Circular Motion

Explain why an astronaut in an orbiting satellite has a feeling of weightlessness.

Chapter: [0.02] Gravitation

State the theorem of parallel axes about moment of inertia.

Chapter: [0.03] Angular Momentum

State the theorem of perpendicular axes about moment of inertia.

Chapter: [0.01] Rotational Dynamics [0.03] Angular Momentum

State Wein's displacement law

Chapter: [0.09] Kinetic Theory of Gases and Radiation

State Wein's displacement law

Chapter: [0.09] Kinetic Theory of Gases and Radiation

State the First law of thermodynamics.

Chapter: [0.09] Kinetic Theory of Gases and Radiation

A particle in S.H.M. has a period of 2 seconds and amplitude of 10 cm. Calculate the acceleration when it is at 4 cm from its positive extreme position.

Chapter: [0.04] Oscillations

The surface tension of water at 0°C is 75.5 dyne/cm. Calculate surface tension of water at 25°C.

(α for water = 2.7×10^{-3}/°C)

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

The spin dryer of a washing machine rotating at 15 r.p.s. slows down to 5 r.p.s. after making 50 revolutions. Find its angular acceleration.

Chapter: [0.01] Circular Motion

Calculate the period of revolution of Jupiter around the Sun. The ratio of the radius of Jupiter’s orbit to that of the Earth’s orbit is 5.

(Period of revolution of the Earth is 1 year)

Chapter: [0.02] Gravitation

Derive an expression for excess pressure inside a drop of liquid.

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

State any four applications of Doppler effect

Chapter: [0.06] Superposition of Waves [0.07] Wave Motion [0.1] Wave Theory of Light

Calculate the average molecular kinetic energy :

(a) per kilomole, (b) per kilogram, of oxygen at 27°C.

(R = 8320 J/k mole K, Avogadro's number = 6*03 x 10^{26} molecules/K mole)

Chapter: [0.04] Oscillations

A uniform steel rod of 5 mm^{2} cross section is heated from 0°C to 25°C. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain.

(α for steel = 12 ^{x} 10^{-6}/°C and γ for steel = 20 x 10^{1O}N/m^{2})

Chapter: [0.05] Elasticity

What are the forced vibrations and resonance?

Chapter: [0.06] Superposition of Waves [0.08] Stationary Waves

Show that only odd harmonics are present in an air column vibrating in a pipe closed at one end.

Chapter: [0.06] Superposition of Waves [0.08] Stationary Waves

A stretched wire emits a fundamental note of frequency 256 Hz. Keeping the stretching force constant and reducing the length of wire by 10 cm, the frequency becomes 320 Hz. Calculate the original length of wire.

Chapter: [0.06] Superposition of Waves [0.08] Stationary Waves

Obtain an expression for potential energy of a particle performing simple harmonic motion. Hence evaluate the potential energy

- at mean position and
- at extreme position.

Chapter: [0.04] Oscillations

Electric field intensity in free space at a distance ‘r’ outside the charged conducting sphere of radius ‘R’ in terms of surface charge density ‘ a ’ is............................

(a)`sigma / in_0[R/r]^2`

(b)`in_0/sigma[R/r]^2`

(c)`R/r[sigma/in_0]^2`

(d)`R/sigma[r/in_0]^2`

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

Instrument which can measure terminal potential difference as well as electro motive force (e.m. f.) is................................

- Wheatstone’s meter bridge
- Voltmeter
- Potentiometer
- Galvanometer

Chapter: [0.13] Current Electricity

If the frequency of incident light falling on a photosensitive material is doubled, then the kinetic energy of the emitted photoelectron will‘be........................................

same as its initial value

two times its initial value

more than two times its initial value

less than two times its initial value

Chapter: [0.04] Oscillations

Linear momentum of an electron in Bohr orbit of H-atom (principal quantum number n) is proportional to..................................

- 1/n
^{2} - 1/n
- n
- n
^{2}

Chapter: [0.18] Atoms, Molecules and Nuclei

In a semiconductor, acceptor impurity is.................................

- antimony
- indium
- phosphorous
- arsenic

Chapter: [0.19] Semiconductors

The power radiated by linear antenna of length T is proportional to........................

(λ= wavelength)

- `lambda/ l`
- `[lambda/l]^2`
- `l/lambda`
- `[l/lambda]^2`

Chapter: [0.2] Communication Systems

The numerical aperture of objective of a microscope is 0.12. The limit of resolution, when light of wavelength 6000A is used to view an object is.......................

- 0.25 * 10
^{-7}m - 2.5 * 10
^{-7}m - 25 * 10
^{-7}m - 250 * 10
^{-7}m

Chapter: [0.11] Interference and Diffraction

Draw a neat and labelled diagram of suspended coil type moving coil galvanometer.

Chapter: [0.14] Magnetic Effects of Electric Current

Define Magnetization

Chapter: [0.15] Magnetism

Define Magnetic intensity.

Chapter: [0.15] Magnetism

Draw a block diagram of generalized communication system.

Chapter: [0.2] Communication Systems

A solenoid 3.142m long and 5.0 cm in diameter has two layers of windings of 500 turns each and carries a current of 5A. Calculate the magnetic induction at its centre along the axis.

Chapter: [0.16] Electromagnetic Inductions

A circular coil of 300 turns and average area 5 * 10^{-}^{3}m^{2} carries a current of 15A. Calculate the magnitude of magnetic moment associated with the coil.

Chapter: [0.15] Magnetism

The magnetic flux through a loop varies according to the relation Φ = 8t^{2} + 6t + C, where ‘C’ is constant, 'Φ' is in milliweber and 't' is in second. What is the magnitude of induced e.m.f. in the loop at t = 2 seconds.

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

An electron is orbiting in 5^{th} Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.

Chapter: [0.18] Atoms, Molecules and Nuclei

Obtain an expression for the radius of Bohr orbit for H-atom.

Chapter: [0.18] Atoms, Molecules and Nuclei

What are α and β parameters for a transistor? Obtain a relation between them.

Chapter: [0.19] Semiconductors

Two metal spheres having charge densities 5μC/m^{2} and -2μC/m^{2} with radii 2mm and 1mm respectively are kept in a hypothetical closed surface. Calculate total normal electric induction over the closed surface.

Chapter: [0.16] Electromagnetic Inductions

The threshold wavelength of silver is 3800Å. Calculate the maximum kinetic energy in eV of photoelectrons emitted, when ultraviolet light of wavelength 2600Å falls on it.

(Planck’s constant, h =6.63 x 1O^{-34}J.s.,

Velocity of light in air, c = 3 x 10^{8} m / s)

Chapter: [0.17] Electrons and Photons

Obtain an expression for e.m.f. induced in a coil rotating with uniform angular velocity in a uniform magnetic field. Show graphically the variation of e.m.f. with time (t).

Resistance of a potentiometer wire is 0.1Ω/cm. A cell of e.m.f 1.5V is balanced at 300 cm on this potentiometer wire. Calculate the current and balancing length for another cell of e.m.f. 1.4V on the same potentiometer wire.

Chapter: [0.16] Electromagnetic Inductions

Describe biprism experiment to calculate the wavelength of a monochormatic light. Draw the necessary ray diagram.

Chapter: [0.11] Interference and Diffraction

If the critical angle of a medium is sin^{-1}(3/5), find the polarising angle.

Chapter: [0.1] Wave Theory of Light

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