May 2011 - Career Point
May 2011 - Career Point May 2011 - Career Point
31. A series R-C circuit is connected to AC voltagesource. Consider two cases ; (A) when C iswithout a dielectric medium and (B) when C isfilled with dielectric of constant 4. The current I Rthrough the resistor and voltage V C across thecapacitor are compared in the two cases. Whichof the following is/are true -A RA R(A) I > I(B) I < IAns.[B,C]RACRBC(C) V > V(D) V < VRCRACRBCSECTION – IIIInteger Answer TypeThis section contains 6 questions. The answer to each ofthe questions is a single-digit integer, ranging from 0 to9. The bubble corresponding to the correct answer is tobe darkened in the ORS33. Two batteries of different emfs and differentinternal resistances are connected as shown. Thevoltage across AB in volts is -6V 1ΩABZ1=R2~⎛ 1 ⎞+ ⎜ ⎟⎝ ωC⎠R24CAns.[5]V A – V B =3V6 3+1 21 1+1 2=2Ω6 +1.5=1.57.51.5= 5V~22 ⎛ 1 ⎞Z2= R + ⎜ ⎟⎝ 4ωC⎠z 1 > z 2 ∴AA I KVC=ωC; VARI < IBCBRBI K= ;4ωCBCV < V32. A thin ring of mass 2 kg and radius 0.5 m isrolling without slipping on a horizontal plane withvelocity 1 m/s. A small ball of mass 0.1 kg,moving with velocity 20 m/s in the oppositedirection, hits the ring at a height of 0.75 m andgoes vertically up with velocity 10 m/s.Immediately after the collision.20 m/s10 m/sAC34. A series R-C combination is connected to an ACvoltage of angular frequency ω = 500 radian/s. Ifthe impendence of the R-C circuit is R 1. 25 , thetime constant (in millisecond) of the circuit is.Ans. [4]Z = R 1 . 25τ = RC2R 2 ⎛ 1 ⎞+ ⎜ ⎟⎝ 500C⎠= Z2R 2 ⎛ 1 ⎞+ ⎜ ⎟⎝ 500C ⎠= R2 × 1. 2522⎛ 1 ⎞⎜ ⎟⎝ 500C ⎠= 0.25 R2 ⇒12500= RC1500C= 0.5RAns.0.75 m1 m/s(A) the ring has pure rotation about its stationaryC.M(B) the ring comes to a complete stop(C) friction between the ring and the ground is tothe left(D) there is no friction between the ring and theground[A,C]1 = RC2500.004 sec = RCRC = 4 mill second.35. A train is moving along a straight line with aconstant acceleration ‘a’. A boy standing in thetrain throws a ball forward with a speed of 10m/s, at an angle of 60º to the horizontal. The boyhas to move forward by 1.15 m inside the train tocatch the ball back at the initial height. Theacceleration of the train, in m/s 2 , is.XtraEdge for IIT-JEE 88 MAY 2011
Ans. [5]2×10×3T == 3 sec2×10x = 10 cos 60° (T) = 5 3 mIn frame of train,5 3 = 21 × a × ( 3 ) 2 + 1.15(a : acceleration of train)a = 5 m/sec 236. Water (with refractive index = 4/3) in a tank is 18cm deep. Oil of refractive index 7/4 lies on watermaking a convex surface of radius of curvature ‘R= 6 cm’ as shown. Consider oil to act as a thinlens. An object ‘S’ is placed 24 cm above watersurface. The location of its image is at ‘x’ cmabove the bottom of the tank. Then ‘x’ is –SAns.[2]R = 6 cmµ = 1.0µ = 7/4µ = 4/3µ 3 µ 1 µ 2 − µ 1 µ 3 − µ 2− = +v u R1R27 4 7 − 1 −4 1 – = 43V − 24 6+ 3 4∞4 1 1 4 1⇒ + = ⇒ =3V 24 8 3V12⇒ V = 16 cm∴ Ans. = (18 –16) cm = 2 cm37. A block of mass 0.18 kg is attached to a spring offorce-constant 2 N/m. The coefficient of frictionbetween the block and the floor is 0.1. Initiallythe block is at rest and the spring is un-stretched.An impulse is given to the block as shown in thefigure. The block slides a distance of 0.06 m andcomes to rest for the first time. The initialvelocity of the block in m/s is V = N/10. Then NisAns.[4]m = 0.18 kgk = 2N/mµ = 0.1Using W – E theorem1 × m(u) 2 1= K (x) 2 + µmg (x)2 21 × (0.18) u 2 1= × 2 × 36 × 10 –4 + 0.1 × 0.1822× 10 × 0.06⇒ u = 0.4 m/sec.4⇒ m/sec.1038. A silver sphere of radius 1 cm and work function4.7 eV is suspended from an insulating thread infree-space. It is under continuous illumination of200 nm wavelength light. As photoelectrons areemitted, the sphere gets charged and acquires apotential. The maximum number ofphotoelectrons emitted from the sphere is A × 10 z(where 1 < A< 10). The value of ‘Z’ is.Ans. [7]1240Energy of photon ≈ eV = 6.2 eV200Maximum KE of a electron = 6.2 eV – 4.7 eVWhen potential on surface of sphere becomesequal to 1.5Vq4π∈ 0= 1.5 V ⇒ q = 1.5 × (4π ε 0 ) × rr1.5 × (4πε0)rNo. of photoelectron emitted n =−191.6 × 10= 1. 04 × 10 7SECTION – IVMatrix match TypeThis section contains 2 questions. Each question hasfour statements (A, B, C and D) given in Column I andfive statements (p, q, r, s and t) in Column II. Anygiven statement Column I can have correct matchingwith ONE or MORE statement(s) given in Column II.For example, if for a given question, statement Bmatches with the statements given in q and r, then forthe particular question, against statement B, darkenthe bubbles corresponds to q and r in the ORS.39. One mole of a monoatomic ideal gas is takenthrough a cycle ABCDA as shown in the P-Vdiagram.Column-II gives the characteristics involved inthe cycle. Match them with each of the processesgiven in Column-I.XtraEdge for IIT-JEE 89 MAY 2011
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31. A series R-C circuit is connected to AC voltagesource. Consider two cases ; (A) when C iswithout a dielectric medium and (B) when C isfilled with dielectric of constant 4. The current I Rthrough the resistor and voltage V C across thecapacitor are compared in the two cases. Whichof the following is/are true -A RA R(A) I > I(B) I < IAns.[B,C]RACRBC(C) V > V(D) V < VRCRACRBCSECTION – IIIInteger Answer TypeThis section contains 6 questions. The answer to each ofthe questions is a single-digit integer, ranging from 0 to9. The bubble corresponding to the correct answer is tobe darkened in the ORS33. Two batteries of different emfs and differentinternal resistances are connected as shown. Thevoltage across AB in volts is -6V 1ΩABZ1=R2~⎛ 1 ⎞+ ⎜ ⎟⎝ ωC⎠R24CAns.[5]V A – V B =3V6 3+1 21 1+1 2=2Ω6 +1.5=1.57.51.5= 5V~22 ⎛ 1 ⎞Z2= R + ⎜ ⎟⎝ 4ωC⎠z 1 > z 2 ∴AA I KVC=ωC; VARI < IBCBRBI K= ;4ωCBCV < V32. A thin ring of mass 2 kg and radius 0.5 m isrolling without slipping on a horizontal plane withvelocity 1 m/s. A small ball of mass 0.1 kg,moving with velocity 20 m/s in the oppositedirection, hits the ring at a height of 0.75 m andgoes vertically up with velocity 10 m/s.Immediately after the collision.20 m/s10 m/sAC34. A series R-C combination is connected to an ACvoltage of angular frequency ω = 500 radian/s. Ifthe impendence of the R-C circuit is R 1. 25 , thetime constant (in millisecond) of the circuit is.Ans. [4]Z = R 1 . 25τ = RC2R 2 ⎛ 1 ⎞+ ⎜ ⎟⎝ 500C⎠= Z2R 2 ⎛ 1 ⎞+ ⎜ ⎟⎝ 500C ⎠= R2 × 1. 2522⎛ 1 ⎞⎜ ⎟⎝ 500C ⎠= 0.25 R2 ⇒12500= RC1500C= 0.5RAns.0.75 m1 m/s(A) the ring has pure rotation about its stationaryC.M(B) the ring comes to a complete stop(C) friction between the ring and the ground is tothe left(D) there is no friction between the ring and theground[A,C]1 = RC2500.004 sec = RCRC = 4 mill second.35. A train is moving along a straight line with aconstant acceleration ‘a’. A boy standing in thetrain throws a ball forward with a speed of 10m/s, at an angle of 60º to the horizontal. The boyhas to move forward by 1.15 m inside the train tocatch the ball back at the initial height. Theacceleration of the train, in m/s 2 , is.XtraEdge for IIT-JEE 88 MAY <strong>2011</strong>
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