If the angular speed of the earth is 7.26 x 10^{–5} rad/s and radius of the earth is 6,400 km,

calculate the change in weight of 1 kg of mass taken from equator to pole.

Concept: Angular Velocity

A small body of mass 0.3 kg oscillates in vertical plane with the help of a string 0.5 m long with a constant speed of 2 m/s. It makes an angle of 60° with the vertical. Calculate tension in the string (g = 9.8 m/s^{2}).

Concept: Definition of Stress and Strain

Two soap bubbles have radii in the ratio 4:3. What is the ratio of work done to blow these bubbles?

Concept: Capillarity and Capillary Action

At what temperature will average kinetic energy of gas be exactly half of its value at N.T.P.?

Concept: Kinetic Theory of Gases- Assumptions

Define surface tension and surface energy.

Concept: Surface Tension

Prove that `g_h=g(1-"2h"/R)` where gh is the acceleration due to gravity at altitude h and h << R (R is the radius of the earth).

Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth

Explain the physical significance of radius of gyration

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

Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road.

Concept: Banking of Roads

Write the necessary equation for maximum safety, speed and state the significance of each term involved in it.

Concept: Banking of Roads

Prove Kirchhoff’s law of radiation theoretically.

Concept: Qualitative Ideas of Blackbody Radiation

Within the elastic limit, find the work done by a stretching force on a wire.

Concept: Elastic Energy

A set of 12 tuning forks is arranged in order of increasing frequencies. Each fork produces

‘Y’ beats per second with the previous one. The last is an octave of the first. The fifth fork

has a frequency of 90 Hz. Find ‘Y’ and frequency of the first and the last tuning forks.

Concept: Formation of Beats

A uniform solid sphere has radius 0.2 m and density 8 x 10^{3} kg/m^{3}. Find the moment of

inertia about the tangent to its surface. (π = 3.142)

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

Define linear simple harmonic motion.

Concept: Simple Harmonic Motion

Assuming the expression for displacement of a particle starting from extreme position, explain graphically the variation of velocity and acceleration w.r.t. time.

Concept: Simple Harmonic Motion

A clock regulated by seconds pendulum, keeps correct time. During summer, length of pendulum increases to 1.005 m. How much will the clock gain or loose in one day?

(g = 9.8 m/s^{2} and π = 3.142)

Concept: Some Systems Executing Simple Harmonic Motion

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

Concept: Study of Vibrations of Air Columns

State the cause of end correction.

Concept: Study of Vibrations of Air Columns

Find the end correction for the pipe open at both the ends in fundamental mode.

Concept: Study of Vibrations of Air Columns

What should be tension applied to a wire of length 1 m and mass 10 gram, if it has to vibrate with fundamental frequency of 50 Hz?

Concept: Forced Oscillations and Resonance

A body of mass ‘m’ performs uniform circular motion along a circular path of radius ‘r’ with velocity ‘v’. If its angular momentum is L, then the centripetal force acting on it is

(A) `(mL^2)/r^3`

(B) `L^2/(mr)`

(c) `L^2/(mr^2)`

(D) `L^2/(mr^3)`

Concept: Centrifugal Forces

If the Earth completely loses its gravity, then for any body _______.

(A) both mass and weight become zero.

(B) neither mass nor weight become zero.

(C) weight becomes zero but not the mass.

(D) mass becomes zero but not the weight.

Concept: Weightlessness

If a rigid body of radius ‘R’ starts from rest and rolls down an inclined plane of inclination

‘θ’ then linear acceleration of body rolling down the plane is _______.

(A)`(gsintheta)/(1+K/R)`

(B) `gsintheta(1+K/R)`

(C) `(gsintheta)/(1+K^2/R^2)`

(D) `gsintheta(1+K^2/R^2)`

Concept: Rolling Motion

1000 tiny mercury droplets coalesce to form a bigger drop. In this process, temperature of the drop _______ .

(A) increases

(B) may increase or decrease

(C) decreases

(D) does not change

Concept: Temperature and Heat

Doppler effect is not applicable when _______.

(A) source and observer are at rest.

(B) there is a relative motion between source and observer.

(C) both are moving in opposite directions.

(D) both are moving in same direction with different velocities

Concept: Beats

Doppler effect is not applicable when _______.

(A) source and observer are at rest.

(B) there is a relative motion between source and observer.

(C) both are moving in opposite directions.

(D) both are moving in same direction with different velocities

Concept: Beats

If the total kinetic energy per unit volume of gas enclosed in a container is E, the pressure exerted by the gas is

(A) E

(B) 3/2 E

(C) `sqrt3E`

(D) 2/3E

Concept: Kinetic Theory of Gases- Assumptions

Two wires of the same material have radii rA and rB respectively. The radius of wire A is twice the radius of wire B. If they are stretched by same load then stress on wire B is

(A) equal to that of A

(B) half that of A.

(C) two times that of A.

(D) four times that of A.

Concept: Eneral Explanation of Elastic Property

Thorium _{90}Th^{232} is disintegrated into lead _{82}Pb^{200}. Find the number of α and β particles emitted in disintegration.

Concept: Alpha-particle Scattering and Rutherford’S Nuclear Model of Atom

If the work function of a metal is 3 eV, calculate the threshold wavelength of that metal.

(Velocity of light = 3 x 10^{8} m/s, Planck’s constant = 6.63 x 10^{–34} J.s.; 1 eV = 1.6 x 10^{–19} J)

Concept: Measurement of Wavelength by Biprism Experiment

Three capacitors of capacities 8 μF, 8 μF and 4 μF are connected in a series and potential difference of 120 volt is maintained across the combination. Calculate the charge on capacitor of capacity 4 μF.

Concept: Reactance and Impedance

If the total energy of radiation of frequency 10^{14} Hz is 6.63 J, calculate the number of photons in the radiation. (Planck’s constant = 6.63 x 10^{–34} J.s.)

Concept: Photoelectric Effect - Hertz’S Observations

Distinguish between diamagnetic and paramagnetic substances

Concept: Magnetic Properties of Materials

Draw a neat, labeled diagram showing different layers of the Earth’s atmosphere.

Concept: Production and Detection of an Amplitude Modulated Wave

Explain the construction of plane wavefront using Huygens’ principle.

Concept: Huygens Principle

Obtain an expression for electric field intensity at a point outside uniformly charged thin plane sheet.

Concept: Effect of Dielectric on Capacity

Write the functions of three segments of a transistor.

Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)

Draw a circuit diagram for studying the input and output characteristics of a n-p-n transistor in common emitter configuration. Using the circuit, explain how input, output characteristics are obtained

Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)

State Ampere’s circuital law.

Concept: Ampere’s Circuital Law

Obtain an expression for magnetic induction along the axis of the toroid.

Concept: Ampere’s Circuital Law

When a resistance of 12 ohm is connected across a cell, its terminal potential difference is balanced by 120 cm length of potentiometer wire. When the resistance of 18 ohm is connected across the same cell, the balancing length is 150 cm. Find the balancing length when the cell is in open circuit. Also calculate the internal resistance of the cell.

Concept: Metre Bridge

Find the ratio of longest wavelength in Paschen series to shortest wavelength in Balmer series.

Concept: Wavelength of an Electron

State the principle on which transformer works.

Concept: Transformers

Explain transformer working with construction.

Concept: Transformers

Derive an expression for e.m.f. and current in terms of turns ratio

Concept: Transformers

Find the magnetization of a bar magnet of length 10 cm and cross-sectional area 4 cm^{2}, if the magnetic moment is 2 Am^{2}.

Concept: Magnetisation and Magnetic Intensity

Derive an expression for path difference in Young’s double slit experiment and obtain the conditions for constructive and destructive interference at a point on the screen.

Concept: Interference of Light Waves and Young’S Experiment

The refractive indices of glass and water w.r.t. air are 3/2 and 4/3 respectively. Determine the refractive index of glass w.r.t. water.

Concept: Polarisation

The logic gate which produces LOW output when one of the input is HIGH and produces

HIGH output only when all of its inputs are LOW is called _______.

(A) AND gate

(B) OR gate

(C) NOR gate

(D) NAND gate

Concept: Digital Electronics and Logic Gates

For efficient radiation and reception of signal with wavelength λ, the transmitting antennas would have length comparable to ______.

(A)`lambda` of frequency used

(B)`lambda/2` of frequency used

(C )`lambda/3` of frequency used

(D)`lambda/4` of frequency used

Concept: Elements of a Communication System

Which one of the following particles cannot be accelerated by a cyclotron?

(A) Electrons

(B) Protons

(C) Deuterons

(D) α- particles

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron

In series LCR circuit at resonance, phase difference between current and e.m.f. of source is ______.

(A) `pi` rad

(B) `pi/2` rad

(C) `pi/4` rad

(D) zero rad

Concept: Resonant Circuit

When unknown resistance is determined by meter bridge, the error due to contact resistance

is minimized ______.

(A) by connecting both the resistances only in one gap.

(B) by interchanging the positions of known and unknown resistance.

(C) by using uniform wire.

(D) by obtaining the null point near the ends of the wire.

Concept: Meter Bridge

The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit is

(A) – 1

(B) 2

(C) 1/2

(D) – 0.5

Concept: Bohr'S Model for Hydrogen Atom

Using monochromatic light of wavelength λ in Young’s double slit experiment, the eleventh dark fringe is obtained on the screen for a phase difference of ______.

(A) `11/2 pi` rad

(B) `21/2 pi` rad

(C) `13 pi` rad

(D) `21 pi` rad

Concept: Interference of Light Waves and Young’S Experiment