Mechanics and Wave Motion ( यांत्रिकी और तरंग गति )

Topics

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Unit I

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Galilean transformations of space and time and their relation to Newton’s laws of motion. Strong and weak form of the Newton’s third law of motion. Difference between Inertial and non-inertial frames. Action-at-a-distance and Mach’s principle. Conclusions of Michelson-Morley experiment. Chief arguments against Galilean relativity. Postulates of Special Relativity. Simple ideas of length contraction and time dilation. Energy and momentum in relativistic mechanics and modification of Newton’s laws of motion. Concepts of gradient, divergence and curl of physical quantities. Simple application of Gauss’s divergence and Stoke’s curl theorems. Conservative and non-conservative forces, Conservation laws for energy and linear momentum and their relation to symmetries. Pseudo-forces in rotating frame. Coriolis force.

Lisl vkSj le; ds xSyhfy;u :ikarj.k vkSj U;wVu ds xfr ds fu;eksa ds lkFk mudk lacaèkA U;wVu ds xfr ds rhljs fu;e dk çcy vkSj nqcZy :iA tM+Roh; vkSj vtM+Roh; Ýse ds chp varjA nwjh ij yxus okys fØ;k vkSj ep dk fl)karA ekbdsylu&e‚yZs ç;ksx ds fu"d"kZA xSyhfy;u lkis{krk ds fo:) eq[; rdZA fo'ks"k lkis{krk ds fl)karA yackbZ ladqpu vkSj le; foLrkj.k ds ljy mik;A vkisf{kd ;kaf=dh esa ÅtkZ vkSj laosx rFkk U;wVu ds xfr ds fu;eksa dk la'kksèkuA HkkSfrd jkf'k;ksa dh izo.krk] fopyu vkSj dyZ dh voèkkj.kkA x‚l ds fopyu vkSj LVksd ds dyZ çes; dk ljy vuqç;ksxA laj{kh vkSj vlaj{kh cy] ÅtkZ vkSj jSf[kd xfr ds fy, laj{k.k fu;e vkSj le:irk ls mudk lacaèkA ?kw.kZu Ýse esa Nn~e cyA dksfjvksfyl cyA

Unit II

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Elastic and inelastic collisions and one and two dimensions. Centre of mass frame as the zero-momentum frame.

Angular momentum, Torque, Conservation of angular momentum and its relation to isotropy of space. Rotational energy and inertia tensor. Moment of inertia for simple bodies (ring, disk, rod, solid and hollow sphere, solid and hollow cylinder,

rectangular lamina). The combined translational and rotational motion of a rigid body on horizontal and inclined planes.

Elasticity, Relations between elastic constants. Twisting of hollow and solid cylinders. Torsional rigidity. Bending moment and Flexural rigidity in bending of beam. Geometrical moment of inertia. Depression for cantilever and supported beams.

çR;kLFk vkSj vçR;kLFk la?kV~V vkSj ,d vkSj nks vk;keA æO;eku Ýse dk dsaæ 'kwU;&xfr Ýse ds :i esaA

dks.kh; laosx] cy vk?kw.kZ] dks.kh; laosx dk laj{k.k vkSj Lisl dh lenSf'kdrk ls lacaèkA ?kw.kÊ ÅtkZ vkSj tM+Ro VsaljA lkèkkj.k fiaMksa ¼fjax] fMLd] j‚M] Bksl vkSj [kks[kys xksys] Bksl vkSj [kks[kys csyu½ ds fy, tM+Ro vk?kw.kZ] vk;rkdkj iVy½A {kSfrt vkSj vkur ryksa ij fdlh n`< fiaM dh la;qDr LFkkukarjh; vkSj ?kw.kZu xfrA

çR;kLFkrk] çR;kLFk fLFkjkad ds chp lacaèkA [kks[kys vkSj Bksl flysaMjksa dk ?kqekoA ejksM+ n`<rkA cadu vk?kw.kZ vkSj cadu ds vk?kw.kZ   esa vkueuh n`<+rkA T;kferh; tM+Ro vk?kw.kZA dSaVhyhoj vkSj lefFkZr cadu ds fy, voueuA

Unit III

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Reduction of a two-body central force problem in to one-body problem. Reduced mass for a pair of bodies. Relative and centre of mass motion with reduced mass. Motion of Planets, satellites and our solar system. Kepler’s laws of planetary motion and their implications. Role of the inverse-square form of Newton’s law of gravitation in determination of orbit. Motion of geo-synchronous and geo-stationary satellites. Elementary concepts of Global Positioning System (GPS) based on relativistic mechanics. Structure and motion of our Galaxy due to self-gravity.

nks&fiaM dsaæh; cy fuesZ; dk ,d&fudk; fuesZ; esa leku;uA fudk;ksa dh ,d ;qXe ds fy, lekuhr æO;ekuA lekuhr æO;eku ds lkFk æO;eku xfr ds lkis{k vkSj dsaæA xzgksa] mixzgksa vkSj gekjs lkSj eaMy dh xfrA dsIyj ds xzgksa dh xfr ds fu;e vkSj muds fufgrkFkZA d{kk ds fuèkkZj.k esa U;wVu ds xq#Rokd"kZ.k ds fu;e ds O;qRØe&oxZ :i dh HkwfedkA Hkw&rqY;dkfyd vkSj Hkw&fLFkj mixzgksa dh xfrA vkisf{kdh; ;kaf=dh ij vkèkkfjr fo’o fLFkfr fu/kkZj.k ra= (GPS) dh çkFkfed voèkkj.kk,aA Lo&xq#Rokd"kZ.k ds dkj.k gekjh vkdk'kxaxk dh lajpuk vkSj xfrA

Unit IV

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Differential equation of simple harmonic motion and its solution. Damped and Forced harmonic oscillations, Sharpness of Resonance. Quality factor. Plane progressive waves in fluid media and pressure and energy distribution along the waves. Transport of energy along strings. Reflection of waves from free and fixed boundaries and phase change at the boundaries. Principle of superposition of waves. Standing waves and resonance. Phase and group velocity.

ljy vkorZ xfr dk vody lehdj.k vkSj mldk gyA voeafnr vkSj ljy vkorhZ nksyu] vuqukn dh rh{.krkA 'kq)rk xq.kd A rjy ek/;e esa lery çxkeh rjax vkSj rjaxksa ds lkFk nkc vkSj ÅtkZ forj.kA Mksfj;ksa ds lkFk ÅtkZ dk vfHkxeuA eqDr vkSj fLFkj ifjlhek ls rjaxksa dk ijkorZu vkSj lhekvksa ij dyk ifjorZuA rjaxksa ds vè;kjksi.k dk fl)karA LFkk;h rjaxsa vkSj vuquknA izkoLFkk vkSj lewg osxA