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7 SAMPLE QUESTION PAPER CLASS NAME & LOGO XII-JEE (MAINS)-YEAR Topic Names: Cicula motion Test Numbe Test Booklet No Wite/Check this Code on you Answe Sheet : IMPORTANT INSTRUCTIONS : Wite this numbe on you Answe Sheet Immediately fill in the paticulas on this page of the Test Booklet with Blue/Black Ball point Pen. Use of pencil is stictly pohibited. The Answe Sheet is kept inside this Test Booklet. When you ae diected to open the Test Booklet, take out the Answe Sheet and fill in the paticulas caefully. The test is of 60 Min. duation. The Test Booklet consists of 30 questions. The maximum maks ae 10. All the Ques. consists of FOUR (4) maks each. PHYSICS- 30 Ques. (10 maks). Candidates will be awaded maks as stated above in Instuction No.5 fo coect esponse of each question. ¼ (one-fouth) maks will be deducted fo indicating incoect esponse of each question. No deduction fom the total scoe will be made if no esponse is indicated fo an item in the Answe Sheet. Use Blue/Black Ball Point Pen only fo witing paticulas/making esponses on Side-1 and Side- of the Answe Sheet. Use of pencil is stictly pohibited. No candidate is allowed to cay any textual mateial, pinted o witten, bits of papes, page, mobile phone, any electonic device, etc., except the Admit Cad inside the examination hall/oom. Rough wok is to be done on the space povided fo this pupose in the Test Booklet only. This space is given at the bottom of each page of the booklet. On completion of the test, the candidate must hand ove the Answe Sheet to the Invigilato on duty in the Room/Hall. Howeve, the candidates ae allowed to take away this Test Booklet with them. The CODE fo this Booklet is A. Make Sue that the CODE pinted on Side- of the Answe Sheet is the same as that on this booklet. In case of discepancy, the candidate should immediately epot the matte to the Invigilato fo eplacement of both the Test Booklet and the Answe Sheet. Do not fold o make any stay maks on the Answe Sheet. No pat of the Test Booklet and Answe Sheet shall be detached unde any cicumstances. Name of the Candidate : Roll Numbe : In figues : In wods : Examination Cente Numbe : Name of Examination Cente (in Capital lettes) : Candidate s Signatue : Invigilato s Signatue :

8 1. The angle tuned by a body undegoing cicula motion depends on time as θ = θ + θ t + θ t. Then the angula 0 1 acceleation of the body is (1) θ 1 () θ (3) θ 1 (4) θ. The maximum and minimum tension in the sting whiling in a cicle of adius.5 m with constant velocity ae in the atio 5 : 3 then its velocity is (1) 7 m/s () 98 m/s (3) 4.9 (4) 490 m/s 3. A bucket full of wate is evolved in vetical cicle of adius m. What should be the maximum time-peiod of evolution so that the wate doesn't fall off the bucket (1) 1 sec () sec (3) 3 sec (4) 6 sec 4. The coodinates of a moving paticle at any time t ae given by x = αt 3 and y = βt 3. The speed of the paticle at time t is given by (1) α + β () t α + β (3) 3t α + β (4) 3t α + β 5. A simple pendulum oscillates in a vetical plane. When it passes though the mean position, the tension in the sting is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the sting with espect to the vetical (1) 10 o () 45 o (3) 60 o (4) 90 o 6. A stone of mass m is tied to a sting and is moved in a vetical cicle of adius making n evolutions pe minute. The total tension in the sting when the stone is at its lowest point is (1) mg () m(g + π n ) (3) m(g + π n ) (4) m{g + ( π n )/ 900} 7. A stone tied with a sting, is otated in a vetical cicle. The minimum speed with which the sting has to be otated (1) Is independent of the length of the sting () Is independent of the mass of the stone (3) Deceases with inceasing in length of the sting (4) Deceases with inceasing mass of the stone 8. A fan is making 600 evolutions pe minute. If afte some time it makes 100 evolutions pe minute, then incease in its angula velocity is (1) 10 π ad/sec () 0 π ad/sec (3) 40 π ad/sec (4) 50 π ad/sec 9. The tension in the sting evolving in a vetical cicle with a mass m at the end which is at the lowest position (1) mg mv () + mg mv (3) mg mv (4) 10. If the equation fo the displacement of a paticle moving on a cicula path is given by 3 ( θ ) = t + 0.5, whee θ is in adians and t in seconds, then the angula velocity of the paticle afte sec fom its stat is (1) 8 ad/sec () 1 ad/sec (3) 4 ad/sec (4) 48 ad/sec 11. A weightless thead can bea tension upto 3.7 kg wt. A stone of mass 500 gms is tied to it and evolved in a cicula path of adius 4 m in a vetical plane. If g = 10ms, then the maximum angula velocity of the stone will be (1) adians/sec () 1 adians/sec (3) 16 adians/sec (4) 4 adians/sec 1. A weightless thead can suppot tension upto 30 N. A stone of mass 0.5 kg is tied to it and is evolved in a cicula path of adius m in a vetical plane. If g = 10m/s, then the maximum angula velocity of the stone will be (1) 10ad/s () 60ad/s (3) 30 ad/s (4) 5 ad/s 13. A kg stone at the end of a sting 1 m long is whiled in a vetical cicle at a constant speed. The speed of the stone is 4 m/sec. The tension in the sting will be 5 N, when the stone is (1) Halfway down () At the bottom of the cicle (3) At the top of the cicle (4) None of the above

9 14. A wheel is subjected to unifom angula acceleation about its axis. Initially its angula velocity is zeo. In the fist sec, it otates though an angle θ 1. In the next sec, it otates though an additional angle θ. The atio of θ / θ 1 is (1) 1 () (3) 3 (4) In a cicus stuntman ides a motobike in a cicula tack of adius R in the vetical plane. The minimum speed at highest point of tack will be (1) gr () gr (3) gr (4) 3gR 16. If the length of the second's hand in a stop clock is 3 cm the angula velocity and linea velocity of the tip is (1) ad/sec., m/sec () ad/sec., m/sec (3) ad/sec., m/sec (4) ad/sec., m/sec 17. In 1.0 s, a paticle goes fom point A to point B, moving in a semicicle of adius 1.0 m (see figue). The magnitude of the aveage velocity is (1) Zeo () 1.0 m/s (3).0 m/s (4) 3.14m/s 18. A peson with his hands in his pockets is skating on ice at the velocity of 10 m/s and descibes a cicle of adius 50 m. What is his inclination with vetical (1) (3) tan tan () tan (1) (4) tan A bob of mass 10 kg is attached to wie 0.3 m long. Its beaking stess is N/m. The aea of coss section of the wie is 10-6 m. The maximum angula velocity with which it can be otated in a hoizontal cicle (1) 1 ad/sec () ad/sec (3) 4 ad/sec (4) 8 ad/sec 0. A cyclist goes ound a cicula path of cicumfeence 34.3 m in sec. the angle made by him, with the vetical, will be (1) 40 o () 45 o (3) 48 o (4) 4 o 1. If a paticle coves half the cicle of adius R with constant speed then (1) Change in K.E. is zeo () Change in K.E. is mv (3) Change in K.E. is 1/ mv (4) Momentum change is mv. A wheel completes 000 evolutions to cove the 9.5 km. distance. then the diamete of the wheel is (1) 1.5 cm () 1.5 m (3) 7.5 m (4) 7.5 cm 3. If a paticle of mass m is moving in a hoizontal cicle of adius with a centipetal foce ( k / ), the total enegy is k k (1) () 4k k (3) (4) 4. Radius of the cuved oad on national highway is R. Width of the oad is b. The oute edge of the oad is aised by h with espect to inne edge so that a ca with velocity v can pass safe ove it. The value of h is (1) (3) v Rgb v b R () (4) v b Rg v R g 5. A paticle of mass m is executing unifom cicula motion on a path of adius. If p is the magnitude of its linea momentum. The adial foce acting on the paticle is (1) m p (3) p m () pm (4) mp 6. The length of second's hand in a watch is 1 cm. The change in velocity of its tip in 15 seconds is π π (1) cm/sec () cm/sec π (3) cm/sec (4) Zeo 30

10 7. A ca is moving on a cicula path and takes a tun. If R 1 and R be the eactions on the inne and oute wheels espectively, then (1) R1 R () R1 > R (3) R1 < R (4) R1 = R 8. Two bodies of mass 10 kg and 5 kg moving in concentic obits of adii R and such that thei peiods ae the same. Then the atio between thei centipetal acceleation is (1) /R () R / (3) /R (4) R / 9. A paticle P is moving in a cicle of adius 'a' with a unifom speed v. C is the cente of the cicle and AB is a diamete. When passing though B the angula velocity of P about A and C ae in the atio (1) 1 : 1 () 1 : (3) : 1 (4) 4 : Two acing cas of masses m 1 and m ae moving in cicles of adii 1 and espectively. Thei speeds ae such that each makes a complete cicle in the same duation of time t. The atio of the angula speed of the fist to the second ca is (1) 1 : () m 1 : m (3) m1 1 : m (4) 1 : 1

11 SAMPLE SOLUTIONS CLASS NAME & LOGO TOPIC NAME: Cicula motion Test No. : Ans: (4) θ d θ Sol: Angula acceleation = = θ dt. Ans: () 98 m/s Sol: In this poblem it is assumed that paticle although moving in a vetical loop but its speed emain constant. mv Tension at lowest point Tmax = + mg mv Tension at highest point Tmin = mg mv T + mg max 5 = = Tmin mv 3 mg by solving we get,v = 4g = = 98 m/s 3. Ans: (3) 3 sec Sol: Minimum angula velocity ω min = π R Tmax = = π ω g 4. Ans: (3) min 3 Sol: x = αt and v dx dt 3t α + β = π = 3s 10 y = β t 3 (given) dy dt x = = 3αt and vy = = 3βt g / R Resultant velocity = v = v + v = 3t α + β 5. Ans: (4) 90 o Sol: Tension at mean position, mv mg + = 3mg v = gl (i) and if the body displaces by angle θ with the vetical then v = gl(1 cos θ ) (ii) Compaing (i) and (ii), cos θ = 0 θ = Ans: (4) Sol: m{g + ( π x n )/900} T = mg + mω = m{g + 4π n } n π n = m g + 4π = m g y 7. Ans: () Is independent of the mass of the stone Sol: Is independent of the mass of the stone 8. Ans: () 0 πad /sec Sol: Incement in angula velocity ω = π(n n ) 1 ad π 600 ad ω = π( ) = 60 s ad = 0π s mv 9. Ans: () + mg Sol: Tension = Centifugal foce + weight mv = + mg 10. Ans: (3) 4 ad/sec dθ d 3 Sol: ω = = (t + 0.5) = 6t dt dt at t = s, ω = 6 () = 4ad/s 11. Ans: (4) 4 adians/sec Sol: Max. tension that sting can bea = 3.7 kgwt = 37N Tension at lowest point of vetical loop = mg + mω = ω 4 = 5 + ω 37 = 5 + w ω = 4 ad/s. 1. Ans: (4) 5 ad /s T max Sol: Tmax = mω max + mg g m = ω max 0.5 = ω ω max = = = 5ad/s 13. Ans: () At the bottom of the cicle mv (4) Sol: mg = 0N and = = 3N 1 It is clea that 5 N tension will be at the bottom of the cicle. Because we know that mv TBottom = mg +

12 14. Ans: (3) 3 1 Sol: Using elation θ = ω 0t + at 1 θ 1 = ( α )() = α (i) (As ω 0 = 0,t = sec ) Now using same equation fo t=4 sec, ω 0 = 0 1 θ 1 + θ = α (4) = 8 α (ii) Fom (i) and (ii), θ 1 = α and θ = 6 α θ = 3 θ Ans: (3) gr Sol: Minimum speed at the highest point of vetical cicula path v = gr 16. Ans: (3) ad/sec., m/sec π π Sol: ω = = = ad/s T 60 and v = ω = = m/s 17. Ans: (3).0 m/s Sol: Aveage Total displacement m velocity = = = ms time 1s 18. Ans: (1) tan 5 Sol: The inclination of peson fom vetical is given by, v (10) 1 1 tan θ = = = θ = tan (1/5) 1 1 g Ans: (3) 4 ad/sec Sol: Centipetal foce = beaking foce mω = beaking stess coss sectional aea mω = p A p A ω = = m ω = 4ad /sec 0. Ans: () 45 o Sol: π = = π and π π v = = T 1. Ans: (1) Change in K.E. is zeo Sol: As momentum is vecto quantity change in momentum P = mvsin( θ /) = mv sin(90) = mv But kinetic enegy emains always constant so change in kinetic enegy is zeo.. Ans: () 1.5 m Sol: Distance coveed in n evolution = n π = nπd 000 π D = 9500 [As n = 000, distance = m] D = = 1.5m 000 π k 3. Ans: () mv k Sol: = k mv = K.E.= 1 mv = k k k P.E. Fd = d = = Total enegy = K.E. + P.E. 4. Ans: () v b Rg Sol: We know that h v Hence = h = b Rg 5. Ans: (3) p m Sol: Radial foce mv] k k k = = v tan θ = and Rg v b Rg mv m p p = = = m m h tan θ = b [As p = π 6. Ans: (1) cm /sec 30 Sol: In 15 second's hand otate though 90. Change in velocity v = vsin( θ/) Angle of binding 1 v θ = tan = 45 g = ( ω )sin(90 / ) π 1 = 1 T 4π π cm = = [As T = 60 sec] sec

13 7. Ans: (3) R1 < R Sol: Reaction on inne wheel 1 v h R1 = M g a 1 v h Reaction on oute wheel R = M g + a whee, = adius of cicula path, a = distance between two wheels and h = height of cente of gavity of ca. 8. Ans: () R / Sol: a ω R T R R = = = a T R R ω R [As T = T R] 9. Ans: () 1 : Sol: Angula velocity of paticle P about point A, v v ω A = = AB Angula velocity of paticle P about point C, v v ω C = = BC ω A v/ 1 Ratio = =. ω v/ C 30. Ans: (4) 1 : 1 Sol: As time peiods ae equal theefoe atio π of angula speeds will be same. ω = T

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CIRCULAR MOTION. Particle moving in an arbitrary path. Particle moving in straight line

CIRCULAR MOTION. Particle moving in an arbitrary path. Particle moving in straight line 1 CIRCULAR MOTION 1. ANGULAR DISPLACEMENT Intoduction: Angle subtended by position vecto of a paticle moving along any abitay path w..t. some fixed point is called angula displacement. (a) Paticle moving