Mechanics and General Properties of Matter (यांत्रिकी और पदार्थ के सामान्य गुण )

Part B-Content of the Course

Total Number of Lectures (in hours): 60

Unit

Topics

Number of Lectures

I

Historical Background and Mathematical Physics

12

1)       Historical Background

1.1)      A brief historical background of mathematics and mechanics in the context of India and Indian culture.

1.2)      A brief biography of Varahamihira and Vikram Sarabhai with their major contribution to science and society.

2)       Mathematical Physics

2.1)      Scalar and vector fields, Gradient of a scalar field and its physical significance.

2.2)      Vector integral – line integral, surface integral and volume integral, Divergence of a vector field and its physical significance, Gauss divergence theorem.

2.3)      Curl of a vector field and its physical significance, Stokes and Green’s theorem, Numerical problems based on the above topics.

Keywords/Tags: Scalar field, Vector field, Vector integral, Gradient, Divergence, Curl.

II

Mechanics of Rigid and Deformable Bodies

12

1)       Rigid Body Mechanics:

1.1)      System of particles and concept of Rigid body, Torque, centre of mass: position of the centre of mass, Motion of the centre of a mass, Conservation of linear and angular momentum with examples, Single stage and multistage rocket.

1.2)      Rotatory motion and concept of moment of inertia, Theorems on moment of inertia: theorem of addition, theorem of perpendicular axis, theorem of parallel axis, Calculation of moment of inertia of rectangular lamina, disc, solid cylinder, solid sphere.

2)       Mechanics of Deformable Bodies:

2.1)      Hook’s law, Young’s modulus, Bulk modulus, Modulus of rigidity and Poisson’s ratio, Relationship between various elastic moduli.

2.2)      Possible values of Poisson’s ratio, Finding Poisson’s ratio of rubber in the laboratory, Torsion of a cylinder, Strain energy of twisted cylinder.

2.3)      Finding the modulus of rigidity of the material of a wire by Barton’s method, Torsional pendulum and Maxwell’s needle, Searl’s method to find g, h and s of the material of a wire, Bending of beam, Cantilever, Beam supported at its ends and loaded in the middle.

Keywords/Tags: Rigid body, Centre of mass, Moment of inertia, Poisson’s ratio.

III

Fluid Mechanics

12

1)       Surface Tension

1.1)      Inter-molecular forces and potential energy curve, force of cohesion and adhesion.

1.2)      Surface tension, Explanation of surface tension on the basis of intermolecular forces, Surface energy, Effect of temperature and impurities on surface tension, Daily life application of surface tension.

1.3)      Angle of contact, The pressure difference between the two sides of a curved liquid surface, Excess pressure inside a soap bubble, Capillarity, determination of surface tension of a liquid – capillary rise method, Jaeger’s method.

2)       Viscosity

2.1)       Ideal and viscous fluid, Streamline and turbulent flow, Equation of continuity, Rotational and irrotational flow, Energy of a flowing fluid, Euler’s equation of motion of a non-viscous fluid and its physical significance.

2.2)       Bernoulli’s theorem and its applications (Velocity of efflux, shapes of wings of airplane, Magnus effect, Filter pump, Bunsen’s burner).

2.3)       Viscous flow of a fluid, Flow of liquid through a capillary tube, Derivation of Poiseuille’s formula and limitations, Stocks formula, Motion of a spherical body falling in a viscous fluid.

IV

Gravitational Potential and Central Forces

12

1)       Gravitational Potential

1.1)       Conservative and non-conservative force field, Conservation of energy in motion under the conservative and non-conservative forces, Potential energy.

1.2)       Conservative force, Conservation of energy, Gravitational potential and gravitational potential energy, Gravitational potential and intensity of gravitational field due to a uniform spherical shell and a uniform solid sphere.

1.3)       Gravitational self-energy, Gravitational self-energy of a uniform spherical shell and a uniform solid sphere.

2)       Central Forces

2.1)   Motion under Central forces, Conservative characteristic of central forces.

2.2)       The motion of a two particles system in Central force, Concept of reduced mass, Reduced mass of positronium and hydrogen.

2.3)       Motion of particles in an inverse-square central force, Motion of celestial bodies derivation of Kepler’s laws. 

2.4)   Elastic and inelastic scattering (elementary idea).

Keywords/Tags: Conservative force field, Gravitational potential, Gravitational self-energy, Central force, reduced mass, Scattering.

V

Relativistic Mechanics and Astrophysics

12

1)       Relativistic Mechanics

1.1)       Frame of references, Galilean transformation, Michelson-Morley experiment.

1.2)       Postulates of special theory of relativity, Lorentz Transformation, Simultaneity and order of events, Length contraction, Time dilation, Relativistic transformation of velocities, Variation of mass with velocity.

1.3)       Mass-energy equivalence and its experimental verification.

2)       Astrophysics

2.1)       Introduction to the Universe, Properties of the Sun, Concept of Astronomical Distance.

2.2)       Life cycle of stars, Chandrasekhar Limit, H-R diagram, Red giant star, White dwarf star, Neutron star, Black hole.

2.3)       Big Bang Theory (elementary idea). 

Keywords/Tags: Transformation, Mass-energy equivalence, Astronomical distance, Chandrasekhar limit, Black hole.

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O;k[;kuksa dh dqy la[;k ¼?kaVs esa½& 60

bdkbZ

fo"k;

O;k[;kuksa dh la[;k

I

,sfrgkfld i`"BHkwfe ,oa xf.krh; HkkSfrdh

12

1)       ,sfrgkfld i`"BHkwfe

1.1)     Hkkjr vkSj Hkkjrh; laLd`fr ds lanHkZ esa xf.kr vkSj ;kaf=dh dk ,d laf{kIr ,sfrgkfld i`"BHkwfe fofoj.kA

1.2)     foKku vkSj lekt esa ojkgfefgj vkSj foØe lkjkHkkbZ ds çeq[k ;ksxnku ds lkFk mudh ,d laf{kIr thouhA

2)       xf.krh; HkkSfrdh

2.1)      vfn'k vkSj lfn'k {ks=] vfn'k {ks= dk xzsfM,aV vkSj HkkSfrd egRoA

2.2)      lfn'k lekdyu& js[kh;] {ks=h; ,oa vk;ru lekdyu] ,d lfn'k {ks= dk MkbotsZal vkSj bldk HkkSfrd egRo] xkWl MkbotsZal çes;A

2.3)      lfn'k {ks= dk dyZ vkSj HkkSfrd egRo] LVksDl ,oa xzhu dk çes;] mijksDr fo"k;ksa ij vk/kkfjr la[;kRed ç'uA

lkj fcanq ¼dh oMZ½@VSx& vfn'k {ks=] lfn'k {ks=] lfn'k lekdyu] xzsfM,aV] MkbotsZal- dyZA

II

n`<+ ,oa fo#I; fudk;ksa dh ;kaf=dh

12

1)       n`<+ fi.M ;kaf=dh

1.1)      d.kksa dk fudk; vkSj n`<+ fi.M dh vo/kkj.kk] cy vk?kw.kZ] nzO;eku dsanz& nzO;eku dsanz dh fLFkfr] nzO;eku dsanz dh xfr] jSf[kd vkSj dks.kh; laosx dk laj{k.k mnkgj.k lfgr] flaxy LVst vkSj eYVhLVst jkWdsVA

1.2)      ?kw.kZu xfr vkSj t+MRo vk?kw.kZ dh vo/kkj.kk] t+MRo vk?kw.kZ çes;&% ;ksx çes;] yEcor v{k çes;] lekarj v{k çes;] ,dleku vk;rkdkj iVy] o`Ùkkdkj pdrh] Bksl flysaMj ,oa Bksl xksys ds t+MRo vk?kw.kZ dh x.kukA

2)       fo#I; fiaMksa dh ;kaf=dh

2.1)      gqd dk fu;e] ;ax çR;kLFkrk xq.kkad] vk;ru çR;kLFkrk xq.kkad] n`<+rk xq.kkad ,oa ikWblu vuqikr] fofHkUu çR;kLFkrk xq.kkadksa esa laca/kA

2.2)      ikWblu fu"ifÙk ds laHkkfor eku] ç;ksx'kkyk esa jcj dk ikWblu vuqikr Kkr djuk] csyu dh ,asBu] ,safBr csyu dh fod`r ÅtkZA

2.3)      ckVZu dh fof/k] ,saBu yksyd ,oa eSDlosy lqbZ }kjk rkj ds inkFkZ dk n`<+rk xq.kkad Kkr djuk] lyZ fof/k }kjk rkj ds inkFkZ dk  g, h ,oa s Kkr djuk] n.M dk cadu] dSaVhyhoj] nksuksa fljksa ij vk/kkfjr rFkk e/; esa Hkkfjr n.MA

lkj fcanq ¼dh oMZ½@VSx& n`<+ fi.M] nzO;eku dsUnz] t+MRo vk?kw.kZ] ikWblu fu"ifÙkA

III

rjy ;kaf=dh

12

1)       i`"B ruko

1.1)      varj&vk.kfod cy vkSj fLFkfrt ÅtkZ oØ] laltd vkSj vklatd cyA

1.2)      varj&vk.kfod cyksa ds vk/kkj ij i`"B ruko dh O;k[;k] i`"B ÅtkZ] i`"B ruko ij rki rFkk v'kqf);ksa dk çHkko] i`"B ruko ds dqN vU; mnkgj.kA

1.3)      Li'kZ dks.k] nzo ds nksuksa oØh; lrgksa ds chp nkckUrj] lkcqu ds cqycqys ds vanj vfrfjDr ncko] dsf'kdkRo nzo ds i`"B ruko dk ekiu& dsf'kdk mUu;u fof/k] tSxj dh fof/kA

2)       ';kurk

2.1)      vkn'kZ vkSj ';ku rjy] /kkjkjs[kh; rFkk fo{kqC/k çokg] lkrR; lehdj.k] ?kw.khZ vkSj v?kw.khZ çokg] çokfgr rjy dh ÅtkZ] v';ku rjy dh xfr dk ;wyj dk lehdj.k ,oe~ bldk HkkSfrd egÙoA

2.2)      cjukSyh çes; vkSj mlds vuqç;ksx ¼cgh& L=ko osx] gokbZ tgkt ds ia[kksa dh vkd`fr] eSxul çHkko] fQYVj iEi] cqUlu cuZj½A

2.3)      rjy dk ';ku çokg] dsf'kdkuyh ds ek/;e ds rjy dk çokg] Iokbtqys lw= dk fuxeu ,oa lhek,a] LVksd lw=] ';ku nzo esa fxjus okys xksykdkj fiaM dh xfrA

lkj fcanq ¼dh oMZ½@VSx& varj&vk.kfod cy] i`"B ruko] Li'kZ dks.k] dsf'kdkRo] ';kurk] ;wyj dk lehdj.k] Iokbtqys lw=A

IV

xq:Roh; foHko vkSj dsanzh; cy

12