notes

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

Concept: Uniform Circular Motion

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

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

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

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

Concept: Definition of M.I., K.E. of Rotating Body

Define emissive power and coefficient of emmision of a body.

Concept: Temperature and Heat

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}]

Concept: Centrifugal Forces

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

Concept: Study of Vibrations of Air Columns

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?

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

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.

Concept: 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..........

(a) vt

(b) (v/D)-t

(c) vt/2D

(d) 2vt/D

Concept: Uniform 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......

(a) W_{1}=W_{2}

(b) W_{1}<W_{2}

(c) W_{1}>W_{2}

(d) W_{1}=W_{2}=0

Concept: Elastic Energy

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 .....

(a) four times that of A.

(b) two times that of A.

(c) three times that of A.

(d) same as that of A.

Concept: Behaviour of Metal Wire Under Increasing Load

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

(a) 0 rad

(b) π/4 rad

(c) π/2 rad

(d) π rad

Concept: Forced Oscillations and Resonance

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 .........

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

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

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

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

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

For polyatomic molecules having 'f' vibrational modes, the ratio of two specific heats,Cp/Cv is..........

(a) `(1+f)/(2+f)`

(b) `(2+f)/(3+f)`

(c) `(4+f)/(3+f)`

(d) `(5+f)/(4+f)`

Concept: Law of Equipartition of Energy

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 ......

(a) 5 m/s

(b) 4 m/s

(c) 3 m/s

(d) 2 m/s

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

Define linear S.H.M.

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

Show that S.H.M. is a projection of U.C.M. on any diameter

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

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.

Concept: Temperature and Heat

Explain analytically how the stationary waves are formed

Concept: Formation of Stationary Waves on String

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

Concept: Formation of Stationary Waves on String

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

Concept: Formation of Beats

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} ]

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

State the theorem of parallel axes about moment of inertia.

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

Prove the theorem of parallel axes about moment of inertia

Concept: Theorems of Perpendicular and Parallel Axes

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

Concept: 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})

Concept: Definition of Stress and Strain

What is 'diffraction of light'

Concept: Fraunhofer Diffraction Due to a Single Slit

Explain two types of diffraction of light.

Concept: Fraunhofer Diffraction Due to a Single Slit

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

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron

Distinguish between ‘paramagnetic’ and ‘ferromagnetic’ substances.

Concept: Magnetic Properties of Materials

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

Concept: Propagation of Electromagnetic Waves

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

Concept: Moving Coil Galvanometer

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}?

Concept: Magnetic Properties of Materials

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

Concept: Inductance - Mutual Inductance

The decay constant of radioactive substance is 4.33 x 10^{-4} per year. Calculate its half life period.

Concept: Radioactivity - Law of Radioactive Decay

If the polarising angle for a given medium is 60°, then the refractive index of the medium is.................

(a) `1/sqrt3`

(b) `sqrt(3/2)`

(c) 1

(d) `sqrt3`

Concept: Polarisation

The resolving power of a telescope depends upon the...............

(a) length of the telescope

(b) focal length of an objective

(c) diameter of an objective

(d) focal length of an eyepiece

Concept: Resolving Power of a Microscope and Telescope

Electric intensity due to a charged sphere at a point outside the sphere decreases with...................

(a)increase in charge on sphere.

(b)increase in dielectric constant.

(c)decrease in the distance from the centre of sphere.

(d)decrease in square of distance from the centre of sphere

Concept: Dielectrics and Polarisation

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 :

(a) `l_1=l_2((R+r)/R)`

(b) `l_1=l_2((R)/(R+r))`

(c) `l_1=l_2((R)/(R-r))`

(d) `l_1=l_2((R-r)/R)`

Concept: Metre Bridge

The energy of photon of wavelength X is_____ .

[h = Planck’s constant, c = speed of light in vacuum]

(a)hcλ

(b)hλ/c

(c)λ/hc

(d)hc/λ

Concept: Einstein’s Equation - Particle Nature of Light

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 |

(a) AND

(b) NOR

(c) OR

(d) NAND

Concept: Digital Electronics and Logic Gates

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

(a) detection

(b) mixing

(c) modulation

(d) attenuation

Concept: Modulation and Its Necessity

State the principle on which transformer works.

Concept: Transformers

Explain transformer working with construction.

Concept: Transformers

Derive an expression for ratio of e.m.f.s and currents in terms of number of turns in primary and secondary coil.

Concept: Transformers

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]

Concept: Mechanical Force on Unit Area of a Charged Conductor

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

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

What is mass defect?

Concept: Mass-Energy Relation and Mass Defect

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 ]

Concept: Photoelectric Effect - Hertz’S Observations

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]

Concept: Reflection and Refraction of Plane Wave at a Plane Surface Using Wave Fronts

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?

Concept: Measurement of Wavelength by Biprism Experiment

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

Concept: Meter Bridge

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

Concept: Oscillators