Date & Time: 24th February 2016, 11:00 am

Duration: 3h

notes

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

Chapter: [0.01] Circular Motion

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

Chapter: [0.02] Gravitation

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

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

Chapter: [0.03] Angular Momentum

Define emissive power and coefficient of emmision of a body.

Chapter: [0.09] Kinetic Theory of Gases and Radiation

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/s^{2}]

Chapter: [0.01] Circular Motion

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

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

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?

Chapter: [0.04] Oscillations [0.05] Oscillations

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.

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

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

Chapter: [0.01] Circular Motion

Two springs of force constants K_{1} and K_{2} (K_{1}> K_{2}) are stretched by same force. If W_{1} and W_{2} be the work done stretching the springs then......

W_{1}=W_{2}

W_{1}<W_{2}

W_{1}>W_{2}

W_{1}=W_{2}=0

Chapter: [0.05] Elasticity

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.

Chapter: [0.05] Elasticity

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

0 rad

`π/4` rad

`π/2` rad

π rad

Chapter: [0.08] Stationary Waves

A sonometer wire vibrates with frequency n_{1} in air under suitable load of specific gravity of . When the load is immersed in water, the frequency of vibration of wire n_{2} will be .........

`n_1sqrt((sigma+1)/sigma)`

`n_1sqrt((sigma-1)/sigma)`

`n_1sqrt(sigma/(sigma+1))`

`n_1sqrt(sigma/(sigma-1))`

Chapter: [0.02] Gravitation

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)`

Chapter: [0.03] Kinetic Theory of Gases and Radiation [0.09] Kinetic Theory of Gases and Radiation

A body of moment of inertia 5 kgm^{2} 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

Chapter: [0.03] Angular Momentum

Define 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

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.

Chapter: [0.09] Kinetic Theory of Gases and Radiation

Explain analytically how the stationary waves are formed

Chapter: [0.08] Stationary Waves

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

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 42^{nd} tuning fork

Chapter: [0.07] Wave Motion

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/s^{2} ]

Chapter: [0.02] Gravitation

State the theorem of parallel axes about moment of inertia.

Chapter: [0.03] Angular Momentum

Prove the theorem of parallel axes about moment of inertia

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

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

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

A steel wire having cross sectional area 1.5 mm^{2} when stretched by a load produces a lateral strain 1.5 x 10^{-5}. Calculate the mass attached to the wire.

(Y_{steel} = 2 x 10^{11} N/m^{2}, Poisson’s ratio σ = 0.291,g = 9.8 m/s^{2})

Chapter: [0.05] Elasticity

What is 'diffraction of light'

Chapter: [0.11] Interference and Diffraction

Explain two types of diffraction of light.

Chapter: [0.11] Interference and Diffraction

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

Chapter: [0.14] Magnetic Effects of Electric Current

Distinguish between ‘paramagnetic’ and ‘ferromagnetic’ substances.

Chapter: [0.11] Magnetic Materials [0.15] Magnetism

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

Chapter: [0.2] Communication Systems

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

Chapter: [0.14] Magnetic Effects of Electric Current

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}?

Chapter: [0.11] Magnetic Materials [0.15] Magnetism

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

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

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

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`

Chapter: [0.1] Wave Theory of Light

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

Chapter: [0.11] Interference and Diffraction

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.

Chapter: [0.12] Electrostatics

In potentiometer experiment, if l_{1} is the balancing length for e.m.f. of cell of internal resistance r and l_{2} 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)`

Chapter: [0.13] Current Electricity

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`

Chapter: [0.17] Electrons and Photons

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

Chapter: [0.19] Semiconductors

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

detection

mixing

modulation

attenuation

Chapter: [0.2] Communication Systems

State the principle on which transformer works.

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

Explain transformer working with construction.

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.

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

A conductor of any shape, having area 40 cm^{2} 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]

Chapter: [0.12] Electrostatics

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

Chapter: [0.18] Atoms, Molecules and Nuclei

What is 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 10^{8} m/s,

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

Chapter: [0.17] Electrons and Photons

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 10^{14} Hz, find the wave number of light in glass.

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

Chapter: [0.1] Wave Theory of Light

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?

Chapter: [0.11] Interference and Diffraction

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

Chapter: [0.09] Current Electricity

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

Chapter: [0.19] Semiconductors

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