The moment of inertia of a thin uniform rod of mass M and length L, about an axis passing through a point, midway between the centre and one end, perpendicular to its length is .....

(a)`48/7ML^2`

(b)`7/48ML^2`

(c)`1/48ML^2`

(d)`1/16ML^2`

Concept: Physical Significance of M.I (Moment of Inertia)

'n' droplets of equal size of radius r coalesce to form a bigger drop of radius R. The energy liberated is equal to...................

(T =Surface tension of water)

`(a) 4piR^2T[n^(1/3)-1]`

`(b) 4pir^2T[n^(1/3)-1]`

`(c) 4piR^2T[n^(2/3)-1]`

`(d)4 pir^2T[n^(2/3)-1]`

Concept: Surface Tension

The buckling of a beam is found to be more if ___ .

(a) the breadth of the beam is large.

(b) the beam material has large value of Young's -modulus.

(c) the length of the beam is small.

(d) the depth of the beam is small.·

Concept: Hooke’s Law

When a transverse wave on a string is reflected from the free end, the phase change produced is ..............

(a) zero rad

(b) ` pi/2 ` rad

(c) `(3pi)/4` rad

(d) `pi` rad

Concept: Reflection of Transverse and Longitudinal Waves

The number of degrees of freedom for a rigid diatomic molecule is.................

(a) 3

(b) 5

(c) 6

(d) 7

Concept: Projection of U.C.M.(Uniform Circular Motion) on Any Diameter

Two particles perform linear simple. harmonic motion along the same path of length 2A and period T as shown in the graph below. The phase difference between them is..............

(a) `zero" "rad`

(b) `pi/4 rad`

(c)`pi/2 rad`

(d) `(3pi)/4 rad`

Concept: Differential Equation of Linear S.H.M.

The light from the Sun is found to have a maximum intensity near the wavelength of 470 nm. Assuming the surface of the Sun as a black body, the temperature of the Sun is .................

[Wien's constant b = 2 .898 x l0^{- 3}mK]

(a) 5800 K

(b) 6050 K

(c) 6166 K

(d) 6500 K

Concept: Temperature and Heat

State Kepler's law of orbit and law of equal areas.

Concept: Kepler’S Laws

A car of mass 1500Kg rounds a curve of radius 250m at 90 Km/hour. Calculate the centripetal force acting on it.

Concept: Dynamics of Uniform Circular Motion - Centripetal Force

Draw a neat labelled diagram for Ferry's perfectly black body.

Concept: Qualitative Ideas of Blackbody Radiation

A mass M attached to a spring oscillates with a period of 2 seconds. If the mass is increased by 2 Kg, the period increases by 1 second. Find the initial mass, assuming

that Hooke's law is obeyed-

Concept: Hooke’s Law

Differentiate between free and forced vibrations .

Concept: Free and Forced Vibrations

The surface tension of water at 0ºc is 75·5 dyne/em. Find surface tension of water at 25°C. [α for water = 0·0021/°C]

Concept: Surface Tension

Derive the relation between surface tension and surface energy per unit area.

Concept: Surface Tension

A wheel of moment of inertia 1 Kgm^{ 2 }is rotating at a speed of 40 rad/s. Due to friction on the axis, the wheel comes to rest in 10 minutes. Calculate the angular momentum of the wheel, two minutes before it comes to rest.

Concept: Physical Significance of M.I (Moment of Inertia)

A particle of mass m, just completes the vertical circular motion. Derive the expression for the difference in tensions at the highest and the lowest points.

Concept: Dynamics of Uniform Circular Motion - Centripetal Force

The Earth is rotating with angular velocity ro about its own axis. R is the radius of the Earth. If Rω^{2} = 0 · 03386 m/ s^{2} , calculate the weight of a body of mass 100 gram at attitude 25°.

(g=9·8m/s^{2}).

Concept: Angular Velocity

Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping.Hence tind kinetic energy for a solid sphere.

Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.

A steel wire-of diameter 1 x 10^{-3}m is stretched by a force of 20 N. Calculate the strain energy per unit volume.(Y steel= 2 x 1011 N /m^{2})

Concept: Definition of Stress and Strain

Define an ideal simple pendulum.

Concept: Some Systems Executing Simple Harmonic Motion

Show that, under certain conditions, simple pendulum performs the linear simple harmonic motion.

Concept: Some Systems Executing Simple Harmonic Motion

A train blows a whistle of frequency 640 Hz in air. Find the difference in apparent frequencies of the whistle for a stationary observer, when the train moves towards and away from the observer with the speed of 72 Km!hour. [Speed of sound in air == 340 m/s.]

Concept: Formation of Beats

With a neat labelled diagram, show that all harmonics are present in an air column contained in a pipe open at both the ends. Define end correction.

Concept: Study of Vibrations of Air Columns

Calculate the kinetic energy of 10 gram of Argon molecules at 127°C.

[Universal gas constant R = 8320 J/k mole K. Atomic weight of Argon = 40]

Concept: Phase of K.E (Kinetic Energy)

In the diffraction pattern due to a single slit of width 'd' with incident light of wavelength 'λ', at an angle of diffraction θ. the condition for first minimum is ....

(a)`lambda sin theta =d`

(b) `d costheta =lambda`

(c)`d sintheta=lambda`

(d) `lambda cos theta=d`

Concept: Fraunhofer Diffraction Due to a Single Slit

Kirchhoff's junction law is equivalent to .............................

(a) conservation of energy.

(b) conservation of charge

(c) conservation of electric potential

(d) conservation of electric flux

Concept: Kirchhoff’s Rules

Let 'p' and 'E' denote the linear momentum and energy of emitted photon respectively. If the wavelength of incident radiation is increased ___ .

(a) both p and E increase

(b) p increases and E decreases

(c) p decreases and E increases

(d) both p and E decrease.

Concept: Qualitative Ideas of Blackbody Radiation

The nuclei having same number of protons but different number of neutrons are called ___ .

(a) isobars

(b) a-particles

(c) isotopes

(d) y-particles

Concept: Hydrogen Spectrum

In case of transistor oscillator, to obtain sustained oscillations, the product of voltage gain without feedback and feedback factor should be ....

(a) zero

(b) less than 1

(c) one

(d) infinity

Concept: Oscillators

The process of regaining of information from carrier wave at the receiver is called .................

(a) modulation

(b) transmission

(c) propagation

(d) demodulation

Concept: Need for Modulation and Demodulation

Reactance of a coil is 157 Ω. On connecting the coil across a source of frequency 100 Hz, the current lags behind e.m.f. by 45°. The inductance of the coil is ...........

(a) 0·25 H

(b) 0·5 H

(c) 4 H

(d) 314H

Concept: Reactance and Impedance

Draw a neat labelled diagram of a parallel plate capacitor completely filled with dielectric.

Concept: The Parallel Plate Capacitor

A point is situated at 7cm and 7·2 cm from two coherent sources. Find the· nature of illumination at the point if wavelength of light is 4000A.

Concept: Fraunhofer Diffraction Due to a Single Slit

Obtain the expression for current sensitivity of moving coil galvanometer.

Concept: Moving Coil Galvanometer

In a cyclotron, magnetic field of 3·5Wb/m2 is used to accelerate protons. What should be the time interval in which the electric field between the Dees be reversed?

(Mass of proton = 1· 67 x 10^{-27}Kg, Charge on proton =1·6x10^{-19}c).

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron

Define magnetization. State its formula and S.I. unit.

Concept: Magnetisation and Magnetic Intensity

Electrostatic energy of 3·5 x 10^{-4} J is stored in a capacitor at 700 V. What is the charge on the capacitor?

Concept: Energy of Charged Condenser

What is space wave propagation?

Concept: Propagation of Electromagnetic Waves

State three components of space wave propagation.

Concept: Propagation of Electromagnetic Waves

Find the value of energy of electron in eV in the third Bohr orbit of hydrogen atom.

(Rydberg's constant (R) = 1· 097 x 10^{7}m ^{- 1},

Planck's constant (h) =6·63x10^{-34} J-s,

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

Concept: Einstein’s Equation - Particle Nature of Light

With the help of neat labelled circuit diagram explain the working of half wave rectifier using semiconductor diode. Draw the input and output waveforms.

Concept: Semiconductor Diode

A cell balances against a length of 200 cm on a potentiometer wire, when it is shunted by a resistance of 8Ω. The balancing length reduces by 40 cm, when it is shunted by a resistance of 4 Ω . Calculate the balancing length when the cell is in open circuit. Also calculate the internal resistance of the cell.

Concept: Metre Bridge

State the law of radioactive decay.

Concept: Radioactivity - Law of Radioactive Decay

Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus

Concept: Radioactivity - Law of Radioactive Decay

The photoelectric work function for a metal is 4.2 eV. If the stopping potential is 3V, find the threshold wavelength and maximum kinetic energy of emitted electrons.

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

Planck's constant = 6·63 x10^{-34} J -s,

Charg.e ori electron = 1·6 x 10 ^{-19} C)

Concept: Photoelectric Effect - Hertz’S Observations

State Faradays laws of electromagnetic induction.

Concept: Faraday’s Law of Induction

State Lenz's Law.

Concept: Lenz’S Law and Conservation of Energy

A circular coil of 250 turns and diameter 18 cm carries a current of 12A. What is the magnitude of magnetic moment associated with the coil?

Concept: Moving Coil Galvanometer

On the basis of Huygens' wave theory of light prove that velocity of light in a rarer medium is greater than velocity of light in a denser medium.

Concept: Huygens Principle

In Young' s experiment the ratio of intensity at the maxima and minima . in the interference pattern is 36 : 16. What is the ratio of the widths of the two slits?

Concept: Interference of Light Waves and Young’S Experiment