Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART I PHYSICS

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1 ena Towe, oad No, Contactos Aea, Bistupu, Jamshedpu 8311, Tel (657)189, IIT JEE 1 hsics ape II AT I HYSICS SECTION I : Single Coect Answe Tpe This Section contains 8 multiple choice questions. Each question has fou choices (A), (B), ( C) and (D) out of which ONLY ONE is coect. 1. A loop caing cuent I lies in the plane as shown in the figue. The unit vecto k ˆ is coming out of the plane of the pape. The magnetic moment of the cuent loop is I a a (A) π ˆ (B) + 1 a I k ˆ a I k (C) π + 1 a I k ˆ (D) (π + 1) a I k ˆ 1. (B) 4 π (a/) µ = I A = I. a k ˆ + π = + 1 Ia k ˆ IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 1 www. penaclasses.com

2 . A thin unifom clindical shell, closed at both ends, is pastiall filled with wate. It is floating veticall in wate in half submeged state. If ρ c is the elative densit of the mateial of the shell with espect to wate, then the coect statement is that the shell is (A) Moe than half filled if ρ c is less than.5 (B) Moe than half filled if ρ c is less than 1. (C) Half filled if ρ c is moe than.5 (D) Less than half filled if ρ c is less than.5. (A) [(V / )+ (AL / )] ρg = ρahg + Vρρ c g [(V / ) + (AL / )] = Ah + ρ c V h = [(V / A) + (L / ) (ρ c V / A)] = [(V / ) ρ c V) (1 / A) + (L / ) if ρ c > (1 / ), h < (L / ) if ρ c < (1 / ), h > (L / ) Whee A : intenal coss sectional aea. IIT JEE 1 (8 Ap 1) uestion & Solutions ape II www. penaclasses.com

3 3. An infinitel long hollow conducting clinde with inne adius / and oute adius caies a unifom cuent densit along its length. The magnitude of the magnetic field, B as a function of the adial distance fom the ais is best epesented b (A) B / (B) B / (C) B / (D) B / 3. (D) Ampee s law (1) / () (3) loop(1) B. dl = B = loop () loop(3) I B. π = µ. π 4 ( / 4 ) µ I = 3 π B µ I B. dl = µ I B = π π 4 4µ I B. π = IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 3 www. penaclasses.com

4 4. Conside a disc otating in the hoizontal plane with a constant angula speed about its cente O. The disc has a shaded egion on one side of the diamete and an unshaded egion on the othe side as shown in the figue. When the disc is in the oientation as shown, two pebbles and ae simultaneousl pojected at an angle towads. The velocit of pojection is in the z plane and is same fo both pebbles with espect to the disc. Assume that (i) the land back on the disc befoe the disc has completed (1 / 8) otation, (ii) thei ange is less than half the disc adius, and (iii) emains constant thoughout. Then O (A) lands in the shaded egion and in the unshaded egion. (B) lands in the unshaded egion and in the shaded egion. (C) Both and land in the unshaded egion. (D) Both and land in the shaded egion. π/4 ' 4. (C) ' V w..t. gound has also velocit along ais while does not has an velocit along ais. As given in figue 1 & 1 ae oughl landed position of pebble & on the disc. 5. A student is pefoming the epeiment of esonance Column. The diamete of the column tube is 4 cm. The fequenc of the tuning fok is 51 Hz. The ai tempeatue is 38 C in which the speed of sound is 336 ms 1. The zeo of the mete scale coincides with the top end of the esonance Column tube. When the fist esonance occus, the eading of the wate level in the column is (A) 14. cm (B) 15. cm (C) 16.4 cm (D) 17.6 cm 5. (B) d = 4 cm, f = 51 Hz T = = 311 C = 336 ms 1 l eff = (L +.3 D) = (λ / 4) = (C / 4f ) L = [336 / (4 51)] = ( ) cm = 15. cm IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 4 www. penaclasses.com

5 6. In the given cicuit, a chage of +8 µc is given to the uppe plate of the 4 µf capacito. Then in the stead state, the chage on the uppe plate of the 3 µf capacito is +8µC 4µF µf 3µF (A) +3 µc (B) +4 µc (C) +48 µc (D) +8 µc 8µF q 1 µf 6. (C) 4µF q 3µF q 1 q q = 8 + q q = + q = 8 3 q = + 48 µc IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 5 www. penaclasses.com

6 7. Two identical discs of same adius ae otating about thei aes in opposite diections with the same constant angula speed. The discs ae in the same hoizontal plane. At time t =, the points and ae facing each othe as shown in the figue. The elative speed between the two points and is v. In one time peiod (T) of otation of the discs, v as a function of time is best epesented b v v (A) T t (B) T t v v (C) T t (D) T t 7. (A) t t V = sin t l ˆ ( = V V ) 8. Two moles of ideal helium gas ae in a ubbe balloon at 3 C. The balloon is full epandable and can be assumed to equie no eneg in its epansion. The tempeatue of the gas in the balloon is slowl changed to 35 C. The amount of heat equied in aising the tempeatue is neal (take = 8.31 J/mol.K) (A) 6 J (B) 14 J (C) 14 J (D) 8 J 8. (D) = [. (5 / ) ] = = J IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 6 www. penaclasses.com

7 SECTION II : aagaph Tpe This section contains 6 multiple choice questions elating to thee paagaphs with two question on each paagaph. Each question has fou choices (A), (B), (C) and (D) out of which ONE is coect. aagaph fo uestions 9 and 1 The β deca pocess, discoveed aound 19, is basicall the deca of a neuton (n). In the laboato, a poton (p) and an electon (e ) ae obseved as the deca poducts of the neuton. Theefoe, consideing the deca of a neuton as a two bod deca pocess, it was pedicted theoeticall that the kinetic eneg of the electon should be a constant. But epeimentall, it was obseved that the electon kinetic eneg has a continuous spectum. Consideing a thee bod deca pocess, i.e. n p + e + v e, aound 193, auli eplained the obseved electon eneg spectum. Assuming the anti neutino ( v e ) to be massless and possessing negligible eneg, and the neuton to be at est, momentum and eneg consevation pinciples ae applied. Fom this calculation, the maimum kinetic eneg of the electon is ev. The kinetic eneg caied b the poton is onl the ecoil eneg. 9. What is the maimum eneg of the anti neutino? (A) Zeo (B) Much less than ev (C) Neal ev (D) Much lage than ev 9. (C) Consideing electon at est. Mass of anti neutino is negligible compaed to mass of poton. So using CLM, velocit of anti neutino is ve lage, almost entie eneg is caied awa b the anti neutino. 1. If the anti neutino had a mass of 3 ev / c (whee c is the speed of light) instead of zeo mass, what should be the ange of the kinetic eneg, K, of the electon? (A) K ev (B) 3. ev K ev (C) 3. ev K < ev (D) K < ev 1. (A) Consideing eplosion of a bod into 3 masses, it is possible to have an one of the thee paticles at est. So K min = & as given in question, K ma = ev if anti neutino emain stationa afte eplosion. IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 7 www. penaclasses.com

8 aagaph fo uestions 11 and 1 Most mateials have the efactive inde, n > 1. So, when a light a fom ai entes a natuall occuing mateial, then b Snell s law, (sin θ 1 / sin θ ) = (n / n 1 ), it is undestood that the efacted a bends towads the nomal. But it neve emeges on the same side of the nomal as the incident a. Accoding to electomagnetism, the efactive inde of the medium is given b the c elation, n = = ± ε µ, whee c is the speed of electomagnetic waves in vacuum, v its v speed in the medium, ε and µ ae the elative pemittivit and pemeabilit of the medium espectivel. In nomal mateials, bothe ε and µ ae positive, impling positive n fo the medium. When both ε and µ ae negative, one must choose the negative oot of n. Such negative efactive inde mateials can now be atificiall pepaed and ae called meta mateials. The ehibit significantl diffeent optical behaviou, without violating an phsical laws. Since n is negative, it esults in a change in the diectioin of popagation of the efacted light. Howeve, simila to nomal mateials, the fequenc of light emains unchanged upon efaction even in meta mateials. 11. Choose the coect statement. (A) The speed of light in the meta mateial is v = c n (B) The speed of light in the meta mateial is n (C) The speed of light in the meta mateial is v = c (D) The wavelength of the light in the meta mateial (λ m ) is given b λ m = λ ai n, whee λ ai is the wavelength of the light in ai. 11. (B) n = (c / v) & speed is positive. 1. Fo light incident fom ai on a meta mateial, the appopiate a diagam is v = c Ai θ1 Ai θ 1 (A) Meta mateial (B) Meta mateial θ θ Ai θ 1 Ai θ 1 (C) Meta mateial θ (D) Meta mateial θ 1. (C) n = (sinθ 1 / sinθ ) sin θ = (sinθ 1 / n) IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 8 www. penaclasses.com

9 aagaph fo uestions 13 and 14 The geneal motion of a igid bod can be consideed to be a combination of (i) a motion of its cente of mass about an ais, and (ii) its motion about an instantaneous ais passing though the cente of mass. These aes need not be stationa. Conside, fo eample, a thin unifom disc welded (igidl fied) hoizontall at its im to a massless stick, as shown in the figue. When the disc stick sstem is otated about the oigin on a hoizontal fictionless plane with angula speed, the motion at an instant can be taken as a comibnation of (i) a otation of the cente of mass of the disc about the z ais, and (ii) a otation of the disc though an instantaneous vatical ais passing though its cente of mass (as is seen fom the changed oientation of points and ). Both thesemotions have the same angula speed in this case. z Now conside two simila sstems as shown in the figue: Case (a) the disc with its face vetical and paallel to z plane; Case (b) the disc with its face making an angle of 45 with plane and its hoizontal diamete paallel to ais. In both the cases, the disc is welded at point, and the sstems ae otated with constant angula speed about the z ais. z z case (a) case(b) Which of the following statements egading the angula speed about the instantaneous ais (passing though the cente of mass) is coect? (A) It is fo both the cases. (B) It is fo case (a); and ( / ) fo case (b). (C) It is fo case (a); and fo case (b). (D) It is fo both the cases. 13. (D) of the igid bod about an point emains same. IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 9 www. penaclasses.com

10 14. Which of the following statements about the instantaneous ais (passing though the cente of mass) is coect? (A) It is vetical fo both the cases (a) and (b) (B) It is vetical fo case (a); and is at 45 to the plane and lies in the plane of the disc fo case (b.) (C) It is hoizontal fo case (a); and is at 45 to the z plane and is nomal to the plane of the disc fo case (b) (D) It is vetical fo case (a); and is at 45 to the zplane and is nomal to the plane of the disc fo case (b) 14. (A) Ais of otation is vetical in both the cases, as is same in both the cases. IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 1 www. penaclasses.com

11 SECTION III : Multiple Coect Answe(s) Tpe This section contains 6 multiple choice questions. Each question has fou choices (A), (B), (C) and (D) out of which ONE O MOE ma be coect. 15. Two solid clindes and of same mass and same adius stat olling down a fied inclined plane fom the same height at the same time. Clinde has most of its mass concentated nea its suface, while has most of its mass concentated nea the ais. Which statement(s) is (ae) coece? (A) Bothe clindes and each the gound at the same time. (B) Clinde has lage linea acceleation than clinde. (C) Both clindes each the gound with same tanslational kinetic eneg. (D) Clinde eaches the gound with lage angula speed. g sin θ a = 15. (D) I 1 + M I > I a < a Also, V = (as) and t = (S / a) V < V and t = (S / a) and t < t and, V = < as V < V 16. A cuent caing infinitel long wie is kept along the diamete of a cicula wie loop, without touching it. The coect statement(s) is (ae) (A) The emf induced in the loop is zeo if the cuent is constant. (B) The emf induced in the loop is finite if the cuent is constant. (C) The emf induced in the loop is zeo it the cuent deceases at a stead ate. (D) The emf induced in the loop is finite if the cuent deceases at a stead ate. 16. (A,B,C,D) o (A,C) Note: [Option (ABCD) is coect povided zeo is consideed as finite else onl (A,C)] About the two sides of the diamete, the magnetic field due to infinite cuent caing wie ae in opposite diection pependicula to the plane of the cicle. Net flu though the cicle is alwas zeo fo constant as well as vaing cuent. IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 11 www. penaclasses.com

12 17. In the given cicuit, the AC souce has = 1 ad/s. Consideing the inducto and capacito to be ideal, the coect choice(s) is (ae) 1µF 1Ω I.5H 5Ω V ~ (A) The cuent though the cicuit, I is.3 A. (B) The cuent though the cicuit, I is.3 A. (C) The voltage acoss 1 Ω esisto = 1 V. (D) The voltage acoss 5 Ω esisto = 1 V. 17. (A,C) o (C) Note: [Option (AC) povided I =.316A.3 A is consideed else onl (C)] X C = (1 / C ) = 1 Ω Z C, = 1 1 j X L = L = 5 Ω Z L, = j Z eq Z. Z = L, C, = 1 Ω Z + Z L, C, 1 I = = =. 316 A 1 1 V 1Ω =. 1 =. 1 = 1 V Z 1 C V 5Ω =. 5 = 1 V Z C 18. Si point chages ae kept at the vetices of a egula heagon of side L and cente O, as shown in the figue. Given that K = (1 / 4πε ) (q / L ), which of the following statement(s) is (ae) coect? F +q S A B +q L O q E q T D q C (A) The electic field at O is 6 K along OD. (B) The potential at O is zeo. (C) The potential at all points on the line is same. (D) The potential at all points on the line ST is same. q kq kq 6 kq 18. (A,B,C) E at = k. +. cos 6 = ( 4 + ) = = 6 K whee, k = 1 / 4πε L L L L V at = (each +ve o ve changes ae equidistant fom ) V on line = Constant V on line ST = Vaing due to position of + q and q IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 1 www. penaclasses.com

13 19. Two spheical planets and have the same unifom densit ρ, masses M and M, and suface aeas A and 4A, espectivel. A spheical planet also has unifom densit ρ and its mass is (M + M ). The escape velocities fom the planets, and, ae V, V and V, espectivel. Then (A) V > V > V (B) V > V > V (C) V / V = 3 (D) V / V = (1 / ) 4 =. 3 = 3 /3. : : = 1 : : 3 /3 V escape = (GM / ) V e : V e : V e = 1 : : 3 /3 19. (BD) M : M : M = 1 : 8 : 9 also, 9 M π ( ) 3 (V / V ) = (1 / ) and V > V > V. The figue shows a sstem consisting of (i) a ing of oute adius 3 olling clockwise without slipping on a hoizontal suface with angula speed and (ii) an inne disc of adius otating anti clockwise the angula speed /. The ing and disc ae sepaated b fictionless ball beaings. The sstem is in the z plane. The point on the inne disc is at a distance fom the oigin, whee O makes an angle of 3 with the hoizontal. Then with espect to the hoizontal suface, z / 3 3 O (A) The point O has a linea velocit 3 i ˆ 11 (B) The point has a linea velocit i ˆ 3 + k ˆ (C) The point has a linea velocit 4 i ˆ 3 4 ˆ k 3 (D) The point has a linea velocit 3 i ˆ + 4. (AB) V = (3) since ICO at bottom point 11 3 V = V + = i ˆ + k ˆ k ˆ 4 IIT JEE 1 (8 Ap 1) uestion & Solutions ape II 13 www. penaclasses.com

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions ) 06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and