May 2011 - Career Point

(A) They will never come out of the magneticfield region(B) They will come out traveling along parallelpaths(C) They will come out at the same time(D) They will come out at different timesAns. [B, D]Sol.× × × ×× × × ×e – v R× p× × ×p× × ×v×× R e × × ×× × × ×2mevevB =R emeVR e =eBRp > Re2mpvevB =R pmpvR p =eBπReπmeTe= =v eB⇒ Tp > TeπmpTp=eB34. A composite book is made of slabs A, B, C, Dand E of different thermal conductivities (given interms of a constant K) and sizes (given in termsof length, L) as shown in the figure. All slabs areof same width. Heat 'Q' flow only from left toright through the blocks. Then in steady state-heat1L3L4L0 1L 5L 6LABCD3K4K5KE6K(A) heat flow through A and E slabs are same(B) heat flow through slab E is maximum(C) temperature difference across slab E issmallest(D) heat flow through C = heat flow through B +heat flow through DAns. [A, C, D]Sol.A4AH2KA2AABCD3 H16H25 H163K4K5KE4AH6KL 4L LAll the three system shown are in series hencerate of heat flow will be same through both A &E.LR A = ;8(KA)4LR D = ;5KA4LR B = ;3KALR E =24KA4LR C = ;8KAUsing parallel combination rate of heat flowacross C = rate of heat flow through B+ rate ofheat flow through D.∆ θ A = HR A =∆ θ∆ θ∆ θ∆ θ3H= R16HL8KA3H ⎛ 4L ⎞= ⎜ ⎟16 ⎝ 3KA ⎠B B=H=2( R )H ⎛ 4L ⎞= ⎜ ⎟2 ⎝ 8KA ⎠C C=5H ⎛ 4L ⎞= ⎜ ⎟16 ⎝ 5KA ⎠D =⎛ L ⎞= H⎜⎟⎝ 24KA ⎠E =HL4KAHL24KAHL4KAHL4KASECTION – IIIParagraph TypeThis section contains 2 paragraphs.. Based upon thefirst paragraph 3 multiple choice question and basedupon on the other paragraph 2 multiple choicequestions have to be answered. Each of these questionshas four choices (A), (B), (C) and (D) out of whichONLY ONE is correct.Paragraph for Questions 35 to 37Phase space diagrams are useful tools inanalyzing all kinds of dynamical problems. Theyare especially useful in studying the changes inmotion as initial position and momentum arechanged. Here we consider some simpledynamical systems in one-dimension. For suchsystems, phase space is a plane in which positionis plotted along horizontal axis and momentum isplotted along vertical axis. The phase spacediagram is x(t) vs p(t) curve in this plane. Thearrow on the curve indicates the time flow. Forexample, the phase space diagram for a particlemoving with constant velocity is a straight line asXtraEdge for IIT-JEE 69 MAY 2011