fiziks Forum for CSIR-UGC JRF/NET, GATE, IIT-JAM, GRE in PHYSICAL SCIENCES

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1 IIT-JAM-8(HYSICS) IMORTAN NOTE FOR CANDIDTES Attept A 5 questios. uestios -5(objective questios) carr si ars each ad questios 6-5(subjective questios) carr twet oe ars each.. The product of a two real, setric atrices ad is (a) setric for all ad (b) ever setric (c) setric if = (d) atistric for all ad. The wor doe b a force i ovig a particle of ass fro a poit (, ) to a eighborig poit ( + d, + d) is give b dw = d + d. The wor doe for a coplete ccle aroud a uit circle is (a) (b) (c) 3 (d) π.3 EFGH is a thi square plate of uifor desit σ ad side 4a. Four poit asses, each of ass, are placed o F the plate as show i the figure. I the oet of itertia atri I of the coposite sste, (a) ol I is zero ( a, a,) ( a, a,) (b) ol I z ad I z are zero ( a, a,) ( a, a,) (c) all the product of itertia ters are zero (d) oe of the product of itertia ters is zero H G.4 The cheical potetial of a ideal Bose gas at a teperature is (a) ecessaril egative (b) either zero or egative (c) eccessaril positive (d) either zero or positive.5 If the electrostatic potetial at a poit (, ) is give b V = ( + 4) volts, the electrostatic eerg desit at that poit (i J/ 3 ) is (a) 5 (b) (c) 4 (d) fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website:

2 .6 I a itertial frae S, a statioar rod aes a agle θ with the -ais. Aother iterial frae S oves with a velocit v with respect to S alog the coo - ais. As observed fro S the agle ade b the rod with the -ais is θ. Which of the followig stateet is correct? (a) θ < θ (b) θ > θ (c) θ < θ if v is egative ad θ > θ if v is positive (d) θ > θ if v is egative ad θ < θ if v is positive.7 Cosider a doped seicoductor havig the electro ad the hole obilities µ ad µ p, respectivel. Its itrisic carrier desit is i. The hole cocetratio p for which the coductivit is iiu at a give teperature is (a) i p (b) i p (c) p i (d) i p.8 Two coheret plae waves of light of equal aplitude, ad each of wavelegths 8, propagatig at a agle of radia with respect to each other, fall 8 alost orall o a scree. The frige-width (i ) o the scree is (a).8 (b).6 (c).8 (d).6.9 A circular disc (i the horizotal -plae) is spiig about a vertical ais through its ceter O with a costat agular velocit. As viewed fro the referece frae of the disc, a particle is observed to eecute uifor circular otio, i the aticlocwise sese, cetered at. whe the particle is at the poit, which of the followig figures correctl represets the directios of the Coriolis force F cor ad the cetrifugal force F cfg? fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website:

3 a F r, F cfg b F r F cfg O O c F cfg F r d F cfg F r O O. The istataeous positio (t) of a sall bloc perforig oe-diesioal daped oscillatios (t) = Ae -rt cos(ωt + a). Here ω is the agular frequec, γ the dapig coefficiet, A the iitial aplitude ad α the iitial phase. If t d ad v, the values of A ad α (with =,,,.) are dt t v v (a) A, (b) A, (c) v A, (d) v A,. A photo of wavelegth λ is icidet o a free electro at rest ad is scattered i the bacward directio. The fuctioal shift i its wavelegth i ters of the Copto wavelegth λc of the electro is C (a) (b) C 3 (c) C (d) C 3 fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website: 3

4 . The logic epressio for the output Y of the followig circuit is Y R S (a) (c) R S (b) R S R S (d) R S.3 The activit of a radioactive saple is decreased to 75% of the iitial value after 3 das. The half-life (i das) of the saple is approiatel [You a use l 3., l 4.4] (a) 38 (b) 45 (c) 59 (d) 69.4 The ratio of the secod-eighbour distace to the earest-eighbour distace i a fcc lattice is (a) (b) (c) 3 (d).5 A therodaic sste is aitaied at costat teperature ad pressure. I therodaic equilibriu, its (a) Gibbs free eerg is iiu (b) ethalp is aiu (c) Helholtz free eerg is iiu (d) iteral eerg is zero fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website: 4

5 SUBJECTIVE UESTIONS.6 A thi hollow clider of radius ad legth both equal to is closed at the botto. A disc of radius / is reoved fro the botto as show i the figure. This object carries a uifor surface-charge desit σ. Calculate the electrostatic potetial at the poit o the ais of the clider as show i the figure. d [ou a use l a. a.7 A particle of ass g is ovig i a cetral force field give b F 3 r r r rˆ. (a) Assuig that the particle is ovig i a circular orbit with agular oetu J-s, fid out the radius of the orbit. () (b) At t =, a additioal force F v, where v is the istataeous velocit of the particle, is switched o. Show that the agetic of its agular oetu after a tie ] () / secod is J s. e.8 A icopressible fluid is eclosed betwee two horizotal surface located at z = ad z = d. The fluid otio is two diesioal, ad the velocit field V, z, t V, z, t u, z, t ˆ w, z, t ˆ is give b z where u, z, t ad w z, t, are periodic fuctios of the horizotal coordiate with waveuber. z w, z, t A t cos si, fid the horizotal velocit d u, z, t usig the equatio of cotiuit. What is the vorticit field V? (5) (a) If the vertical velocit d z (9) fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website: 5

6 d (b) Fid the et fluid flu fro a parallelepiped of size as show i the figure, where. (6).9 The wave fuctio Ψ () of a particle cofied to a oe-diesioal bo of legth with rigid walls is give b si, =,, 3,.. (a) Deterie the eerg eigevalues. Also, deterie the eigevalues ad the eige fuctios of the oetu operator. (5) (b) Show that the eerg eigefuctios are ot the eigefuctios of the oetu operator. (6).. A ass ad sprig sste cosists of two bloc of ass (<M). These blocs are coected with two idetical sprigs with sprig costat as show i the figure. The sste is costraied to ove alog a straight lie o a frictioless horizotal surface. The sprig follows Hooe s law. Fid the agular frequecies of the idepedet oscillatios (oral odes). M M Now, the asses M ad are iterchaged ad the ew arrageet is show i the followig figure: M The ratio of the ew arrageet to that of the old arrageet, whe the iddle bloc reais statioar, is. Fid the ratio of the frequecies i the two arrageets whe the iddle bloc oscillates. () fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website: 6

7 . A half-wave plate ad a quarter-wave plate are placed betwee a polarizer ad a aalzer. All of these are parallel to each other ad perpedicular to the directio of propagatio of upolarized icidet light (see the figure). The optic-ais of the half-wave plate aes a agle of 3 with respect to the pass-ais of ad that of the quarterwave plate is parallel to the pass-ais of. z Half-wave uarter-wave plate plate (a) Deterie the state of polarizatio for the light after passig through (i) the half-wave plate ad (ii) the quarter-wave plate. (5) (b) What should be the orietatio of the pass-ais of with respect to that of such that the itesit of the light eergig fro is aiu? (6). Cosider a sste of N o-iteractig distiguishable spi- ½ particles, each of agetic oet. The sste is at a equilibriu teperature T i a agetic field B such that particles have their agetic oets aliged parallel to B. (a) Fid the eerg E ad the etrop S of the sste. (9) (b) Usig the relatioship betwee E ad S, fid T. Hece deterie the ratio N i ters of µ, B ad T. [Use l N! = N l N N] ().3 (a) A ideal gas, ept i cotact with a heat reservoir, udergoes a quasistatic process i which its pressure gets doubled. Obtai the Mawell relatio fro the differetial for df = - S dt dv ad evaluate the epressio for the chage i etrop of oles of the gas. (9) fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website: 7

8 (b) Usig S = S(T, V), derive a geeral epressio for ( U/ V) T, where U(S,V) is the iteral eerg. Evaluate it for the ideal gas as cosidered i part (a). Justif that the outcoe is cosistet with the epressio for the average eerg ow fro the ietic theor. ().4 Cosider a ideal Feri gas cosistig of N o-relativistic spi- particles cofied to a legth i oe diesio at K. (a) Fid a epressio for the desit of states ad hece calculate the Feri eerg of the gas. (5) (b) Fid the ea eerg per particle i ters of the Feri eerg. (6).5 A square loop of side ad ass M is ade of a wire of cross-sectioal area A ad resistace R. The loop, ovig with a costat velocit eters a regio havig costat agetic field B ˆ. v oˆ i i the horizotal -plae, a b v o iˆ z d c B (a) Fid a epressio for the -copoet of the force F actig o the loop i ters of its velocit v t, B, ad R. () (b) Fid the speed of the loop as its side ad eits the field regio at = ad setch its variatio with. (9) fizis c/o Aad Istitute of atheatics, 8-B/6 Jia Sarai hoe: , Website: 8

Engineering Mechanics Dynamics & Vibrations. Engineering Mechanics Dynamics & Vibrations Plane Motion of a Rigid Body: Equations of Motion

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