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8 Questions<strong>Solution</strong>Set # 12Physics Challenging ProblemsPublished in this Issue1.[C] Magnetic field due to infinite current carryingµ Jsheet is given by B = 0, where J is linear current2density.II IIIµ 0 J2µ 0 J2µ 0 J2µ 0 J2(a) (b)Fig. (a) and (b) represent the direction of magneticfield due to current carrying sheets. For x < a,µ 0Jµ 0J(2J)µ 0 (3J) µ 0 (4J)Bresul tant = − − +2 2 2 2For a < x < 2a,µ 0Jµ 0 (2J) µ 0 (3J) µ 0 (4J)tant = − − + = −2 2 2 2For 2a < x < 3a,µ 0Jµ 0 (2J) µ 0 (3J) µ 0 (4J)Bresul tant = + − − = 02 2 2 2So, the required curve isBBresul µ 0Oa 2a 3a 4a 5aXJ(C) This situation is similar to part (i)(D) In a uniform electric field, path can be only3. A → Q B → R C → P D → Q(A) At t = 1s, flux is increasing in the inwarddirection, hence induced e.m.f. will be inanticlockwise direction.(B) At t = 5s, there is no change in flux, so inducede.m.f. is zero(C) At t = 9s, flux is increasing in upward directionhence induced e.m.f. will be in clockwise direction.(D) At t = 15s, flux is decreasing in upwarddirection, so induced e.m.f. will be inanticlockwise direction.4.[A, B, D]Rate of work done by external agent isde/dt = BIL.dx/dt = BILv and thermal powerdissipated in resistor = eI = (BvL) I clearly both areequal, hence (A).If applied external force is doubled, the rod willexperience a net force and hence acceleration. As aresult velocity increase, hence (B).Since, I = e/ROn doubling R, current and hence required powerbecome half.Since, P = BILvHence (D)2. A → P,Q,S B → P,Q,R,SC → P,Q,R,S D → Q(A) Velocity of the particle may be constant, if forcesof electric and magnetic fields balance eachother. Then, path of particle will be straight line.Also, path of particle may be helical if magneticand electric fields are in same direction. But pathof particle cannot be circular. Path can becircular if only magnetic field is present, or ifsome other forces is present which can cancel theeffect of electric field.(B) Here, all the possibilities are possible dependingupon the combinations of the three fields.5.[A]→∧^jxzn 1 sini = n 2 sinr→1.5(µ 1×j) = 2( µ 2×j)∧∧∧1.5(a i + b j) × j = 2[(c i + d j) × j]∧=∧1 .5a k 2c ka 20 4= =c 1.5 3∧∧∧∧XtraEdge for IIT-JEE 18 APRIL 2010
6.[A]I 2f–f sin60º f cos60º +fI 1xu = -f cos60ºf = +f1 1 1= −f v − f cos 60º1 1 2= +f v f1 2 1− =f f vv = -ff = cos 60ºxf= xcos 60ºx = 2f∴ final image will formed at optical centre of firstlens.7.[C] C v = (3 + 2T)RdQ = dU + PdVadiabatic process dQ = 00 = Rn (3 + 2T)dT + PdVnRT0 = Rn(3 + 2T)dT + dVVdV ⎛ 3 + 2T ⎞∫−= ∫⎜⎟dTV ⎝ T ⎠– log V = 3 logT + 2T + C– logV – logT 3 = 2T + Clog VT 3 = 2T + CVT 3 = e 2TVT 3 e -2T = C8.[A] P = P 0 − αVPV = RTRT2= P 0 − αVV3P0 V αVT = −R RdT = 0dV2P03αV− =R R0PV = 03 α2Now put V in T.• Saturn’s rings are made up of particles of ice, dustand rock. Some particles are as small as grains ofsand while others are much larger thanskyscrapers.• Jupiter is larger than 1,000 Earths.• The Great Red Spot on Jupiter is a hurricane-likestorm system that was first detected in the early1600’s.• Comet Hale-Bopp is putting out approximately250 tons of gas and dust per second. This isabout 50 times more than most comets produce.• The Sun looks 1600 times fainter from Pluto thanit does from the Earth.• There is a supermassive black hole right in themiddle of the Milky Way galaxy that is 4 milliontimes the mass of the Sun.• Halley’s Comet appears about every 76 years.• The orbits of most asteroids lie partially betweenthe orbits of Mars and Jupiter.• Asteroids and comets are believed to be ancientremnants of the formation of our Solar System(More than 4 billion years ago!).• Comets are bodies of ice, rock and organiccompounds that can be several miles in diameter.• The most dangerous asteroids, those capable ofcausing major regional or global disasters, usuallyimpact the Earth only once every 100,000 yearson average.• Some large asteroids even have their own moon.• Near-Earth asteriods have orbits that cross theEarth’s orbit. These could potentially impact theEarth.• There are over 20 million observable meteorsper day.• Only one or two meteorites per day reach thesurface of Earth.• The largest found meteorite was found in Hoba,Namibia. It weighed 60 tons.XtraEdge for IIT-JEE 19 APRIL 2010
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(C) Pressure at A > pressureat B(D)
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7. Experimental verification of New
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28. Assertion : A rocket moves forw
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60. Point out the incorrect stateme
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MOCK TEST - BIT-SATTime : 3 Hours T
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40. A body of mass 2 kg is being dr
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10. The foci of a hyperbola coincid
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LOGICAL REASONING1. Fill in the bla
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SOLUTION FOR MOCK TESTIIT-JEE (PAPE
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or 0.1 v α + 1 = 2 + 2 × 10 -2 ×
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1.[C]2.[B]3.[B]SOLUTION FOR MOCK TE
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CAREER POINTIn associationwithLaunc
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