IIT-JEE 2006 Solutions by MOMENTUM (questions based on memory of students) PHYSICS

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1 II-JEE 006 Solutions by MOMENUM (questions based on memory of students) PHYSIS II-JEE 006 INSRUIONS: (i) Question no. to has only one correct option. You will be awarded marks for right answer and mark for wrong answer. (ii) Question no. to 0 has one or more than one correct option(s). You will be awarded marks if you answer all correct options and only correct option(s) and mark will be awarded for wrong answer. (iii) (iv) (v) Question no. to are based on small write up first go through it then answer these questions. You will be awarded marks for right answer and marks for wrong answer. Question no. to 6 are subjective problems. ircle their correct answers. here is no negative marking for it. Each question carries 6 marks. Question no. 7 to 40 carry 6 marks each. hese may have more than one correct options. here is no negative marking for these.. 4π g student measures g N number of times. he error is Δ in and Δ in. Which will give best result? (a) Δ 0., Δ 0., N 0 (b) Δ 0., Δ 0., N 0 (c) Δ 0., Δ 0.0, N 0 (d) Δ 0., Δ 0.0, N 0 Δg Δ Δ + g In option (d) error in Δg is minimum and number of repetition of measurement are maximum. In this case the error in g is minimum. (d). Parallel rays of light from Sun falls on a biconvex lens of focal length f and the circular image of radius r is formed on the focal plane of the lens. hen which of the following statement is correct? (a) rea of image is πr and area is directly proportional to f (b) rea of image is πr and area is directly proportional to f (c) Intensity of image increases if f is increased. (d) If lower half of the lens is covered with black paper area will become half. (b). he string between mass m and m is inextensible. If the string is cut find the magnitudes of accelerations of mass m and m (a) g, g (b) g, g/ (c) g/, g (d) g/, g/ m Initially the spring force Kx mg (before the string is cut) Just after the string is cut, for block m Kx - mg ma mg - mg ma a g/ For block of mass m, mg ma or a g (c) m MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

2 4. If current I is flowing through B. hen the correct relationship is r B I r l/ l/ II-JEE 006 (a) V B V B (b) Power across B is 4 times the power across B. (c) urrent densities in B and B are equal. (d) Electric field due to current inside B and B are equal. l l R ρ ρ πr R B :R B : : 4 4 V :V IR : IR : 4 P j B B B B B :PB I R B :I R B : j I I : B B B B B : E B VB : VB E : 4 : 4 : 4. Focal length of the plano-convex lens is cm. he object is at as shown in the figure. he plane side is silvered. he image is (a) 60 cm to the left of lens (b) cm to the left of lens (c) 60 cm to the right of lens (d) 0 cm to the left of lens 0 cm Focal length F of equivalent mirror is given by + + or F f f e m F cm he equivalent mirror will concave mirror of focal length cm. Now for a spherical mirror, + v u F v 0 v v - cm 6. Double star system consists of two stars and B which have time period and B, B Radius R and R BB and mass M and M B. B hoose the correct option. > R BB (b) (a) If > B B then R If > B B then M R (c) B R (d) B B B For binary star the time period of two stars are equal. (d) > M BB MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

3 II-JEE In the arrangement shown, calculate from where the mass should be hanged so that wire () vibrates in second harmonic and wire () in first harmonic? (a) (b) 4 (c) 4 (d) l 4 B M D v λf μ μ f f 4 + Mg Mg/ Στ B B 0 Mg l (Mg/) l / (a) 8. he graph between object distance (u) and image distance (v) is as shown in the figure. What is the focal length of the convex lens? (a).00 cm, ±0.0 cm (b).00 cm, ±0.0 cm (c) 0. cm, ± 0.0 cm (d) 0. cm, ±0.0 cm l Mg (v) 0 (-u) (-9, 9) v + f f v u v Δv 0. Δf 0. 0 cm (a) 9. he circular scale of a screw gauge has 0 divisions and pitch of 0. mm. Find the diameter of sphere. Main scale reading is. 0 MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

4 4 II-JEE 006 (a). (b). (c).0 (d). ns. (a) 0. Find the time constant for the given R circuits in correct order. R V V V R R R R R Ω, R Ω, 4 μf, μf (a) 8, 4, 8/9 (b) 8, 8/9, 4 (c) 4, 8, 8/9 (d) 4, 8/9, 8 τ eq R eq. eq τ ( + )( + 4) 8 μs 4 8 τ. μs τ.( 4 + ) 4 μs +. Ra undergoes radioactive decay with half life 4 days. What is the probability that a nucleus 87 undergoes decay in two half lives (a) (b) / (c) /4 (d) /4 ( ln ) ( ) ( λt λ ) ln Required probability e e e e 4 (c). solid sphere of mass M and radius R having moment of inertia I about its diameter is recast into a solid disc of radius r and thickness t. he moment of inertia of the disc about an axis about the edge and perpendicular to the plane is I. he relation between radius R and r (a) r R (b) r R (c) r R (d) r R Moment of inertia of sphere I MR Moment of inertia of disc about an axis passing through its edge and perpendicular to its plane Mr I I cm + Mh + Mr Mr MR Mr or r R R 4 MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

5 . urrent I is flowing out from the plane of paper. steady state current I is flowing in the loop BD. (a) he net force is zero (b) he net torque is zero (c) s seen from O, the loop will rotate in clockwise along OO axis (d) s seen from O, the loop will rotate in anticlockwise direction along OO axis. O I B II-JEE 006 D he magnetic force on B and D part of the loop will be zero because on this part d l ρ and B ρ are parallel and anti-parallel. he magnetic force on B part will act upward and on D part the force is of equal magnitude but in downward direction. hese two forces will produce a torque in clockwise sense when viewed from O. (a) & (c) I O 4. solid cylinder is rolling down the inclined plane without slipping. Which of the following is/are correct? (a) he friction force is dissipative (b) he friction force is necessarily changing (c) he friction force will aid rotation but hinder translation (d) he friction force is reduced if θ is reduced θ cceleration of center of mass of cylinder g sin θ g sin θ g sin θ a cm f mg sin θ I cm MR / + + MR MR θ gsin θ Since Mg sin θ f Ma cm M Mg sin θ f So, if θ is reduced friction f will also decrease. he work done by friction will be zero since point of application of friction force is instantaneously at rest. Hence frictional force is not dissipative. Since frictional force is static, its value can lie from 0 to μmg cos θ but not necessarily equal to μmg cos θ. he frictional force will provide torque for rotation but it will oppose translation. (c), (d). he following field line do not represent (a) induced electric field (b) magnetostatic field (c) Gravitational field of a mass at rest (d) electrostatic field (c), (d) MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

6 6. he graph between the stopping potential (V o ) and wave number (/λ) is as shown in the figure. φ is the work function, then (a) φ : φ : φ : : 4 (b) φ : φ : φ 4 : : (c) tan θ hc/e where θ is the slope (d) ultraviolet light can be used to light photoelectrons from metal and metal only 6 II-JEE 006 MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404 V o Metal Metal Metal φ φ φ θ θ θ hc hc hc φ : φ : φ : : : : λ o λ o λ o λ o λ o λ o : : 4 From Einstein's photoelectric equation hc hc φ φ + ev s V s λ eλ e hc herefore slope tan θ e 0.00 nm - λ o λ 000 nm 0000 Å o 0.00 nm - λ o λ 00 nm 000 Å o nm - λ o λ 0 nm 00 Å o Hence UV light can be used to eject photoelectrons from all the metals, and. (a), (c) 7. he ball rolls down without slipping (which is at rest at a) along ab having friction. It rolls to a maximum height h c where bc has no friction. K a, K b and K c are a c kinetic energies at a, b and c. (a) K a K c, h a h c (b) K b > K c, h a h h a c b (c) K b > K c, h a < h c (d) K b > K c, h a > h c h c Since part bc is frictionless, torque on the ball on this part is zero and hence its angular velocity will be constant on this part. Further from conservation of mechanical energy h c < h a. (d) 8. black body of temperature is inside chamber of o temperature initially. Now the closed chamber is slightly opened to sun such that temperature of black body () and chamber ( o ) o remains constant. (a) Black body will absorb more radiation. (b) Black body will absorb less radiation (c) Black body emit more energy (d) black body emit energy equal to energy absorbed by it Since the temperature of the black body is constant. So heat absorbed heat radiated. (d) 9. y sin ωt + B cos ωt + sin ωt cos ωt. For what value of, B and it will represent SHM (a) for all value of, B and ( 0) (b) B, B (c) -B, B (d) B, 0 λ

7 7 II-JEE 006 y sin ωt + B cos ωt + sin ωt cos ωt. B y ( cos ωt) + ( + cos ωt) + sin ωt B B y + + cos ωt + sin ωt By the above equation, we can find that option (a), (b) and (c) are correct for represent SHM. (a), (b) & (c) 0. Spherical symmetric charge system centered at origin. Electric potential Q φ 4πεoR o r R o Q φ 4πε o r r > R o (a) spherical symmetry at r R o encloses a net charge Q (b) Electric field is discontinued at r R o (c) hange is only present at r R o φ R o r (d) Electrostatic energy is zero for r < R o dφ For r > R o, E dr Qo 4 πε r Passage I harge enclosed by the concentric spherical surface of r R o Q ε o φ εoe 4π r εo 4πr Q 4πεor d φ For r < R o, E 0 (Θ c constant) dr dφ For r > R o, E 4 dt πε Qo r Since for r < R o, E 0, hence charge will be only on the spherical surface of r R o. For r < R o, E 0 energy density ε o E 0 (a), (b), (c) and (d) y cos (0.πx - 00πt) y cos (0.46πx - 9πt). How many time is a second does a stationary observer hears loud sound (maximum intensity) (a) 4 (b) 8 (c) 0 (d) ω 00 π ω 9π f 0 Hz, f 46 Hz π π Beat frequency f - f 4 (a). What is velocity of sound wave? (a) 00 m/s (b) 80 m/s (c) 00 m/s (d) 94 m/s v ω/k 00π/(0. π) 00 (a). t x 0, how many times does the net amplitude between 0 in s (a) 46 (b) 4 (c) 0 (d) 00 MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

8 t x 0, y y + y cos 96 πt cos 4πt For y 0, cos 96 πt 0 or cos 4πt 0 96 πt (n + ) (π/) and 4πt (m + ) π/ For 0 < t < 8 II-JEE < n < 9. and - < m <. Here n and m are integers, therefore net amplitude becomes zero 00 times. (d) Passage II he density of block is ρ/ and is used to block a hole H. 4. If liquid of density ρ is filled in the apparatus find out h (h is the height of upper surface of water level from the top of the block) so that cylinder just starts rising. (a) h h (b) h h (c) h h (d) h h he net upward force on block due to pressure P πr - P 6πr ρg(h + h) πr - ρgh 6πr ρgh πρ ρgh 4πr he block will rise if ρg 4πr (h - h ) > 6πr h(ρ/)g 4 (h - h ) > h h P o 4r h ρ/ h r r P o h P 6πr r 6πr h(ρ/)g h P πr > h h h. If the water level is lowered such that it comes below the top of the block keeping the block constant at which height h (h is depth of the upper surface of water level from the top of the block) will the block be at a stable condition? (a) 4h h (b) 9 h h (c) h h (d) 9 h h he upward force on block due to pressure P πr + (h ) ρgh πr ρgh πr 6πr h(ρ/)g 6h 4h h 9 (a) h P πr 6πr h(ρ/)g 6. If water level is lowered below h, then (a) the block will not rise (b) the block will start rising again at h h/ (c) the block will start rising again at h h/ (d) the block will start rising again at h h/ MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

9 9 II-JEE 006 If water level is further decrease below h the upward force on block due to pressure will become less that the weight of block, therefore, the block will not rise. (a) Passage III 7. In the given circuit, initially S is closed and S is open then if maximum charge is Q o V Q o (a) harge Q in time t τ (b) harge Q Q o ( - e - ) in time t τ R S (c) work done by battery energy dissipated in resistor. (d) harge Q Q o ( - e - ) in time t τ S In one time constant the charge on capacitor is 6% of maximum charge. t t τ, Q Q o ( - e -τ/τ ) Q o ( - e - ) 8. In the above - circuit the charge Q on capacitor at any time can hold a value π π (a) Q Qo cos ωt (b) Q Qo cos + ωt d Q (c) Q dt (d) Q Q Q o cos ωt and d Q Q dt (from KV) (c) 9. fter S is closed, then which one is correct? (a) he current always flows in one direction (b) he energy is exchanged between the capacitor and the inductor (c) he energy initially is magnetic (d) he value of a maximum instantaneous current I V From energy conservation, I V I V Passage IV Passage was very lengthy and could not be retrieved.. If 0.0 kg steam at 7 K is mixed with 0.4 kg ice at -0 o then find the resultant temperature. Heat required to melt the entire ice msδ m k cal. Maximum heat which can be supplied by steam m + msδ kcal herefore the entire ice will not melt hence the resultant temperature of mixture will be 0 o. 4. Determine the value of n for which the de-broglie wavelength corresponding to nth orbit is equal to wavelength of nth line of ymann series. Given Z. MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404 d dt Q

10 0 de Broglie wavelength of electron in the nth orbit is given by πr nλ πr π n 0 λ 0. 0 m n n Z Wavelength of nth line of ymann series is given by RZ λ ( ) n + Since λ λ π 0. n Z Solving this we get n ( n + n ) ( n + ) n + n } n 0-0 / { ( ) n + II-JEE 006. disc is kept on a smooth horizontal plane with its plane parallel to horizontal plane. groove is made in the disc as shown in the figure. he coefficient of friction between a mass m inside the groove and the surface of the groove is / and sin θ /. Find the acceleration of mass with respect to the frame of reference of the disc. a o m/s θ f μ( N + N' ) f m( a sin θ + g) and f a' a cosθ m m/s a o m/s μn+n N θ ma o 6. If n number of balls each of mass m collide elastically with the plate of mass M per second with a velocity v elastically and reflect back. Find the velocity of balls such that plate is at equilibrium. Given: n 00, m 0.0 kg, M kg b v a Force applied by striking balls rate of change of momentum n mv For equilibrium net torque should be zero. b b Mg n mv 4 Mg 0 v 0 m/s nm Match the following 7. olumn olumn (a) ngular magnification (P) Dispersion of lenses (b) Sharpness of the image (Q) f o and f e (c) ight gathering power (R) perture of lenses MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

11 (d) ength of telescope (S) Spherical aberration (a) P Q R S (b) P Q R S (c) P Q R S (d) P Q R S II-JEE olumn olumn (a) Fission (P) Matter - energy (b) Fusion (Q) In atoms of high atomic number only (c) β - decay (R) In atoms of low atomic number only (d) Exothermic nuclear (S) Involves weak nuclear forces (a) P Q R S (b) P Q R S (c) P Q R S (d) P Q R S 9. olumn olumn (a) Uniformly charged ring (P) Electric field is present (b) dielectric ring with uniformly distributed (Q) Magnetic field is present charge is rotating with constant angular velocity. (c) wire carrying constant current (R) Induced electric field is present (d) I I o cos ωt (S) Magnetic moment is present. (a) P Q R S (b) P Q R S (d) P Q R S (d) P Q R S 40. olumn olumn (a) JK process (P) ΔW > 0 (b) K process (Q) ΔW < 0 (c) M process (R) ΔQ > 0 (d) MJ process (S) ΔQ < 0 P 0 0 J M 0 K 0 0 V (a) P Q R S (b) P Q R S (c) P Q R S (d) P Q R S MOMENUM,, Wright own, Jabalpur (M.P.), Ph.(076) 4008, 404

IIT-JEE 2012 PAPER - 1 PART - I : PHYSICS. Section I : Single Correct Answer Type

IIT-JEE 2012 PAPER - 1 PART - I : PHYSICS. Section I : Single Correct Answer Type IIT-JEE PAPER - PART - I : PHYSICS Section I : Single Correct Answer Type This section contains multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is