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Kinematics (QB).pdf
Kinematics (QB).pdf
Kinematics (QB).pdf
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Kinematics (QB).pdf
Kinematics (QB).pdf
Kinematics (QB).pdf
Kinematics (QB).pdf
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Kinematics (QB).pdf
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Kinematics (QB).pdf
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Kinematics (QB).pdf
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Kinematics (QB).pdf
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Kinematics (QB).pdf

  1. QUESTION BANK ON KINEMATICS
  2. SHORT QUESTIONS Q.1 Avector  a isturnedwithoutachangeinitslengththroughasmallangled.Whatare  a anda? Q.2 Does the speedometer of a car measure speed or velocity? Explain. Q.3 When a particle moves with constant velocity, its average velocity, its instantaneous velocity and its speedareall equal. Comment on this statement. Q.4 Inagiventimeinterval,isthetotaldisplacementofaparticleequaltotheproduceoftheaveragevelocity andthetimeinterval, evenwhenthe velocityisnot constant? Explain. Q.5 Can you have zero displacement and a nonzero average velocity? Can you have a zero displacement and a nonzerovelocity? Illustrate your answer on a x-t graph. Q.6 At whichpoint on its path a projectile has thesmallest speed? Q.7 Apersonstandingon theedgeof acliffat someheight abovetheground belowthrows oneball straight upwithinitialspeeduandthenthrowsanotherballstraightdownwiththesameinitialspeed.Whichball, if either, has the larger speedwhenit hits theground? Neglect air resistance. Q.8 An airplane on flood relief mission has to drop a sack of rice exactly in the center of a circle on the ground whileflyingatapredeterminedheightand speed. What issodifficult about that? Whydoesn't it just drop the sack whenit is directlyabove the circle. Q.9 Water is collecting in a bucket during a steadydownpour. Will the rate at which the bucket is filling change ifasteadyhorizontal windstarts to blow? Q.10 Show that, takingthe Earth's rotation and revolution into account, a book resting on your table moves faster atnight than it doesduringthe daytime. Inwhat reference frameis this statementtrue? Q.11 Whichofthefollowinggraphscannotpossibilyrepresentonedimensionalmotionofaparticle? Q.12 Canyousuggestasuitablesituationfrom observationaround you foreachofthefollwing?
  3. Q.13 Oneofthefollowingstatementsis incorrect. (a) The car traveled around the track at a constant velocity. (b) The car traveled around the track at a constant speed. Which statement is incorrect and why? Q.14 Giveanexamplefrom your own experience in whichthevelocityofan objectis zero forjustan instant of time,but its acceleration isnot zero. Q.15 A ball is dropped from rest from the top of a building and strikes the ground with a speed vf . From groundlevel,asecond ballisthrownstraightupwardatthesameinstantthatthefirstballisdropped.The initialspeedofthesecondballisv0 =vf ,thesamespeedwithwhichthefirst ballwilleventuallystrikethe ground. Ignoringair resistance, decide whether the balls cross paths at half the height of the building, abovethehalfwaypoint, orbelowthehalfwaypoint. Giveyourreasoning. Q.16 Themuzzlevelocityofagunisthevelocityofthebulletwhenitleavesthebarrel.Themuzzlevelocityof oneriflewith a short barrelis greater than themuzzlevelocityof anotherrifle that has aloner barrel. In whichrifleistheaccelerationofthebulletlarger? Explainyourreasoning. Q.17 On a riverboat cruise, a plastic bottle is accidentally dropped overboard. A passenger on the boat estimate that the boat pulls ahead of the bottle by5 meters each second. Is it possible to conclude that the boat is moving at 5 m/s with respect tothe shore?Account for your answer. Q.18 Awrenchis accidentallydroppedfromthe topof themast ona sailboat.Will thewrench hit at thesame placeonthedeckwhetherthesailboatis atrestormovingwitha constant velocity?Justifyyouranswer. Q.19 Is theacceleration of aprojectileequal to zero whenit reaches thetop of its trajectory? Ifnot, whynot? Q.20 Achildis playingonthefloorofarecreationalvehicle(RV)as itmoves alongthehighwayat aconstant velocity.Hehas atoycannon,which shoots amarbleat afixedangleandspeed with respectto thefloor. The cannon can be aimed toward the front or the rear of the RV. Is the range toward the front the same as,lessthan,orgreaterthantherangetowardtherear?Answerthis question(a)from thechild'spoint of viewand(b)from the point ofview ofan observer standingstill on the ground.Justifyyouranswers. Q.21 Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across ariverintheleasttime. SwimmerAswimsperpendiculartothecurrentandlands on thefarshore downstream, because the current has swept him in that direction. Swimmer B swims upstream at an angle to the current and lands on the far shore directlyopposite the starting point. Swimmer C swims downstream at an angle to the current in an attempt to take advantage of the current. Who crosses the riverinthe least time?Account for your answer.
  4. ONLY ONE OPTION IS CORRECT. Take approx. 2 minutes for answering each question. Q.1 If positiontime graph ofaparticle is sine curveas shown, whatwillbeitsvelocity-timegraph. (A) (B) (C) (D) Q.2 A truck startingfrom rest moves with anacceleration of 5 m/s2 for 1 sec and thenmoveswithconstantvelocity.Thevelocityw.r.tgroundv/s time graph forblock in truck is (Assume that block does not fall off the truck) (A) (B) (C) (D) None of these Q.3 If angularvelocityof adisc depends an angle rotated  as = 2 + 2, then its angular acceleration at  = 1 rad is : (A) 8 rad/sec2 (B) 10 rad/sec2 (C) 12 rad/sec2 (D) None Q.4 If a particle takes t second less and acquires a velocity of v ms–1 more in falling through the same distance (starting from rest) on two planets where the accelerations due to gravity are 2 g and 8 g respectivelythen: (A) v = 2gt (B) v = 4gt (C) v = 5 gt (D) v = 16 gt Q.5 It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him 3 minuteto walk up . How longwill it take for the passenger to arrive at the top if he walks up themovingescalator? (A) 30 sec (B) 45 sec (C) 40 sec (D) 35 sec Q.6 The co-ordinates of a moving particleat a time t, are give by, x = 5 sin 10 t, y= 5 cos 10t. The speed of the particle is : (A) 25 (B) 50 (C) 10 (D) None Q.7 Tangential accelerationofaparticlemovinginacircleofradius1mvarieswith timetas(initialvelocityofparticleiszero).Timeafterwhichtotalaccelerationof particle makes andangleof 30° with radial acceleration is (A) 4 sec (B) 4/3 sec (C) 22/3 sec (D) 2 sec Q.8 Aparticleisprojectedfrom ahorizontalplane(x-zplane)suchthatitsvelocityvectorattimetisgivenby j ˆ ) ct b ( î a V     . Its rangeon the horizontal planeis given by (A) ba c (B) 2ba c (C) 3ba c (D) None
  5. Q.9 Aparticle moves along a straight line in such a way that it’s acceleration is increasing at the rate of 2 m/s3. It’s initial acceleration and velocitywere 0, the distance covered byit in t =3 second is. (A) 27 m (B) 9 m (C) 3 m (D) 1 m Q.10 Aballisthrownverticallydownwithvelocityof5m/s.Withwhatvelocityshouldanotherballbethrown down after 2 seconds so that it can hit the 1st ball in 2 seconds (A) 40 m/s (B) 55 m/s (C) 15 m/s (D) 25 m/s Q.11 Accelerationversusvelocitygraphofaparticlemovinginastraightline startingfromrestisasshowninfigure.Thecorrespondingvelocity-time graph would be (A) (B) (C) (D) Q.12 Aparticle is projected verticallyupwards from a pointAon the ground.It takes t1 timeto reach a point Bbut it stillcontinues tomoveup. Ifit takes furthert2 timeto reach thegroundfrom point Bthen height ofpoint Bfrom thegroundis (A) 2 2 1 ) t t ( g 2 1  (B) g t1 t2 (C) 2 2 1 ) t t ( g 8 1  (D) 2 1 g t1 t2 Q.13 Balls arethrownverticallyupwardinsuch awaythatthe next ball isthrownwhen the previousone is at themaximumheight.Ifthemaximumheightis5m,thenumberofballsthrown perminutewillbe (A) 40 (B) 50 (C) 60 (D) 120 Q.14 Thevelocity-timegraphofabodyfallingfrom restundergravityandreboundingfrom asolidsurfaceis representedbywhichofthefollowinggraphs? (A) (B) (C) (D) Q.15 Adiscarrangedinavertical planehastwogrovesofsamelength directedalong the vertical chordAB and CD as shown in the fig.The same particles slide down alongAB and CD.The ratio of the time tAB /tCD is (A) 1 : 2 (B) 1 : 2 (C) 2 : 1 (D) 2 : 1 Q.16 Themagnitudeofdisplacementofaparticlemovingina circleofradius awith constantangularspeed varies withtimet as (A) 2 a sint (B) 2a sin 2 t  (C) 2a cos t (D) 2a cos 2 t  Q.17 Abodymoves withvelocityv=nxm/s wherexis itsposition.Thenetforceactingon bodyiszeroat (A) 0 m (B) x = e2 m (C) x = e m (D) x = 1 m
  6. Q.18 AbodyAis thrown vertically upwards with such a velocity that it reaches a maximum height of h. Simultaneouslyanother bodyB is droppedfrom height h. It strikes the ground and does not rebound. The velocityofArelative to Bv/s timegraph is best represented by: (upwarddirection is positive) (A) (B) (C) (D) Q.19 A bodyofmass 1 kg is acted upon bya force j ˆ t 3 cos 3 î t 3 sin 2 F      find its position at t = 1 sec if at t = 0 it is at rest at origin. (A)         2 2 9 2 , 3 3 (B)         2 2 3 2 , 3 2 (C)         2 3 2 , 3 2 (D) none of these Q.20 A force F = Be–Ct acts on a particle whose mass is m and whose velocity is 0 at t = 0. It’s terminal velocityis: (A) mB C (B) C m B (C) m BC (D) – mC B Q.21 Aman moves in x-yplane along the path shown.At what point is his average velocityvectorinthesame directionas his instantaneous velocityvector.The man starts from point P. (A)A (B) B (C) C (D) D Q.22 Theaccelerationofaparticlewhichmoves alongthepositivex-axis varies with its position as shown. If the velocityof the particle is 0.8 m/s at x = 0 , the velocityof the particle at x = 1.4 is(in m/s) (A) 1.6 (B) 1.2 (C) 1.4 (D) none of these Q.23 Abodyisthrownupin alift withavelocityu relativetotheliftand thetimeofflight is foundtobet. The accelerationwithwhichtheliftismovingupis (A) t gt u  (B) t gt u 2  (C) t gt u  (D) t gt u 2  Q.24 Aball is thrown verticallydownwards with velocity gh 2 from a height h.After colliding with the ground it justreaches thestartingpoint. Coefficientofrestitution is (A) 1 2 (B) 1/2 (C) 1 (D) 2 Q.25 Thegraphofpositionxversustimetrepresentsthemotionofaparticle. Ifbandcarebothpositiveconstants,whichofthefollowingexpressions best describes the acceleration a of the particle? (A) a = b – ct (B) a = + b (C) a = – c (D) a = b + ct
  7. Q.26 Twostonesarethrownupverticallyandsimultaneouslybutwithdifferentspeeds.Whichgraphcorrectly representsthetimevariationoftheirrelativepositionsx.Assumethatstones donotbounceafterhitting ground. (A) (B) (C) (D) Q.27 A particle of mass 1 kgis acted upon bya force 'F' which varies as shown in thefigure. If initial velocity of theparticleis10 ms–1,the maximumvelocityattainedbytheparticleduringtheperiodis (A) 210 ms–1 (B) 110 ms–1 (C) 100 ms–1 (D) 90 ms–1 Question No. 28 to 32 Two ballsAand B are thrownwith same velocityufrom the top ofa tower. BallAis thrown vertically upwards andthe ball B isthrownverticallydownwards. Q.28 Choose thecorrect statement (A) BallB reaches the groundwithgreatervelocity (B) BallAreaches the groundwithgreatervelocity (C)Both theballs reach the groundwith same velocity (D) Cannot be interpreted Q.29 If tA and tB are the respective times taken bythe ballsAand B respectively to reach the ground, then identifythecorrect statement (A) tA > tB (B) tA = tB (C) tA < tB (D) Cannot be interpreted Q.30 If tA = 6 s and tB = 2 s, then the height of the tower is (A) 80 m (B) 60 m (C) 45 m (D) none of these Q.31 Thevelocityuofeach ball is (A) 10 ms–1 (B) 15 ms–1 (C) 20 ms–1 (D) none of these Q.32 IfaballCis thrownwiththesamevelocitybutinthehorizontal directionfrom thetop ofthetower, then it will reach thegroundintimetc equal to (A) 4 s (B) 3.46 s (C) 4.2 s (D) none of these Question No. 33 to 36 Thex-t graphofaparticlemovingalongastraight lineisshown in figure Q.33 The v-t graph of the particle is correctlyshown by (A) (B) (C) (D)
  8. Q.34 The a-t graph of the particle is correctlyshown by (A) (B) (C) (D) Q.35 Thedistance-time graphofthe particle is correctlyshown by (A) (B) (C) (D) Q.36 The speed-time graph of the particle is correctlyshown by (A) (B) (C) (D) Question No. 37 to 43 Thefigureshowsavelocity-timegraphofaparticlemoving alongastraightline Q.37 Choose the incorrect statement. The particle comes to rest at (A) t = 0 s (B) t = 5 s (C) t = 8 s (D) none of these Q.38 Identifytheregioninwhichtherateofchangeofvelocity t v    oftheparticleis maximum (A) 0 to 2s (B) 2 to 4s (C) 4 to 6 s (D) 6 to 8 s Q.39 If the particle starts from the position x0 =–15 m, then its position at t = 2s will be (A) –5 m (B) 5 m (C) 10 m (D) 15 m Q.40 Themaximum displacementoftheparticleis (A) 33.3 m (B) 23.3 m (C) 18.3 m (D) zero Q.41 The totaldistance travelled bythe particle is (A) 66.6 m (B) 51.6 m (C) zero (D) 36.6 m Q.42 The correct acceleration-timegraph of the particleis shown as (A) (B) (C) (D)
  9. Q.43 Thecorrect displacement-timegraph of the particleis shown as (A) (B) (C) (D) Q.44 Aball isthrownfrom a pointon ground at someangle of projection.At thesame time abird starts from apointdirectlyabovethispointofprojectionataheighthhorizontallywithspeedu.Giventhatinitsflight ball just touches the bird at one point. Find thedistance on ground whereball strikes (A) 2u h g (B) u 2h g (C) 2u 2h g (D) u h g Q.45 Aball isprojectedfrom top ofatowerwith avelocityof 5 m/s at anangleof530 to horizontal.Its speed when it is at a height of 0.45 m from the point of projection is : (A) 2 m/s (B) 3 m/s (C) 4 m/s (D)datainsufficient. Q.46 Average velocityofa particle is projectilemotion between its startingpoint and thehighest point of its trajectoryis : (projection speed = u, angle of projection from horizontal= ) (A) u cos (B)   2 cos 3 1 2 u (C)   2 cos 2 2 u (D)   2 cos 1 2 u Q.47 Findtimeofflightofprojectilethrownhorizontallywithspeed50ms–1 fromalonginclinedplanewhich makes anangle of  =45° from horizontal. (A) 2 sec (B) 2 2 sec (C) 2 sec (D) none Q.48 Particleisdroppedfromthe heightof20m fromhorizontal ground.Thereiswindblowingdueto which horizontalaccelerationoftheparticlebecomes6ms–2 .Findthehorizontaldisplacementoftheparticletill it reaches ground. (A) 6 m (B) 10 m (C) 12 m (D) 24 m Q.49 Aballisdroppedfromheight5m.Thetimeafterwhichballstopsreboundingifcoefficient ofrestitution between ball and ground e = 1/2, is (A) 1 sec (B) 2 sec (C) 3 sec (D)infinite Q.50 A ball is hit by a batsman at an angle of 37° as shown in figure. The man standingatPshouldrunatwhatminimumvelocitysothathecatchestheball before it strikes the ground. Assume that height of man is negligible in comparisontomaximumheightofprojectile. (A) 3 ms–1 (B) 5 ms–1 (C) 9 ms–1 (D) 12 ms–1 Q.51 Aprojectileisfiredwithaspeeduatananglewiththehorizontal.Itsspeedwhenitsdirectionofmotion makes anangle‘’withthehorizontalis (A) u sec cos (B) u sec sin (C) u cos sec (D) u sin  sec Q.52 A projectile is fired with a velocityat right angle to the slope which is inclined at an angle  with the horizontal. TheexpressionfortherangeR alongtheinclineis (A)  sec g v 2 2 (B)  tan g v 2 2 (C)  sec tan g v 2 2 (D)  2 2 tan g v
  10. Q.53 Aparticleisprojectedverticallyupwards fromOwithvelocityvandasecondparticleisprojected at the sameinstantfromP(ataheighthabove O)withvelocityvatanangleofprojection.Thetimewhenthe distancebetweenthemisminimumis (A)  sin v 2 h (B)  cos v 2 h (C) h/v (D)h/2v Q.54 A ball is projected from ground with a velocityV at an angle  to the vertical. On its path it makes an elasticcollisonwitha vertical wall andreturns toground. Thetotaltimeofflightoftheballis (A) g sin v 2  (B) g cos v 2  (C) g 2 sin v  (D) g cos v  Q.55 Two particles are moving along two long straight lines, in the same plane, with the same speed = 20 cm/s.The angle between the two lines is 60°, and their intersection point is O.At a certain moment, the two particles are located at distances 3m and 4m from O, and are moving towards O. Subsequently,theshortest distance between them will be (A) 50 cm (B) 40 2 cm (C) 50 2 cm (D) 50 3 cm Q.56 Inthefigureshown,thetwoprojectiles are firedsimultaneously.Theminimum distancebetweenthemduringtheirflightis (A) 20 m (B) 10 3 m (C) 10 m (D) None Q.57 A shell fired from the base of a mountain just clears it. If  is the angle of projection then the angular elevationofthesummit is (A) 2 1  (B) tan–1(1/2) (C) tan–1(1/2 tan ) (D) tan–1(2 tan ) Q.58 If time taken bythe projectile to reach Q is T, than PQ = (A)Tvsin (B) Tv cos  (C) Tv sec  (D) Tv tan  Q.59 Aparticle is projected at angle 60° with speed 3 10 , from the point ‘A’as shown in the figure.At the sametimethewedge is madeto movewith speed 3 10 towards rightas shown in thefigure. Then the timeafterwhichparticlewillstrikewithwedgeis (A) 2 sec (B) 3 2 sec (C) 3 4 sec (D) None Q.60 Aball isheld in theposition shownwithstringof length 1 m just taut & then projected horizontallywithavelocityof3m/s.Ifthestringbecomestautagainwhenitis vertical, angle  isgivenby (A) 53° (B) 30° (C) 45° (D) 37° Q.61 Two projectilesAand B arethrown with the samespeed such thatAmakes angle  with the horizontal and Bmakes angle  withthevertical, then (A)Bothmusthavesametimeofflight (B)Bothmustachievesamemaximumheight (C)Amust have more horizontalrange than B (D)Bothmayhavesametimeofflight
  11. Q.62 ParticlesAandBaremovingwithconstant velocitiesalongxandyaxisrespectively,the graphofseparationbetweenthem withtimeis (A) (B) (C) (D) Q.63 Anaeroplaneflyingataconstantvelocityreleasesabomb.Asthebombdropsdownfromtheaeroplane, (A)itwill always beverticallybelow theaeroplane (B)itwillalways beverticallybelowtheaeroplane onlyiftheaeroplaneisflyinghorizontally (C)itwillalwaysbeverticallybelowtheaeroplane onlyiftheaeroplaneisflyingatan angleof45°tothe horizontal (D)itwillgraduallyfallbehindtheaeroplaneiftheaeroplaneisflyinghorizontally Q.64 Two particles are projected simultaneouslyin the same vertical plane,from the same point on ground, butwithsamespeeds butatdifferent angles (<90° )to thehorizontal.Thepath followed byone,as seen bythe other, is (A)averticalstraight line (B)astraightlinemakingaconstant anglewiththehorizontal (C) a parabola (D) a hyperbola Q.65 Supposeaplayerhits several baseballs. Whichbaseball will bein the air forthe longest time? (A) The onewith thefarthest range. (B)Theonewhichreachesmaximum height. (C)Theonewiththegreatestinitial velocity. (D) The one leaving the bat at 45° with respect to the ground. Question No. 66 to 69 Twoprojectilesarethrownsimultaneouslyinthesameplanefromthesamepoint.Iftheirvelocitiesarev1 and v2 at angles1 and 2 respectivelyfrom the horizontal, thenanswerthe followingquestions Q.66 The trajectoryof particle 1 withrespect to particle 2 will be (A) a parabola (B)astraightline (C)avertical straight line (D)ahorizontal straightline Q.67 If v1cos1 = v2cos2, then choose the incorrect statement (A)one particlewill remainexactlybelow or above theother particle (B) the trajectoryof one with respectto other will be avertical straight line (C)bothwill have the samerange (D) none of these Q.68 If v1sin1 = v2sin2, then choosethe incorrect statement (A)thetimeofflight ofboththeparticles willbesame (B)the maximumheightattainedbytheparticleswill besame (C)the trajectoryof one with respect to another will be ahorizontal straight line (D) none of these Q.69 If v1 = v2 and 1 > 2, then choose the incorrect statement (A) Particle 2 moves under the particle 1 (B) The slope of the trajectoryof particle 2 with respect to 1 is always positive (C) Both the particle will have the same range if 1 > 45° and 2 < 45° and 1 + 2 = 90° (D) none of these
  12. Question No. 70 to 75 Aprojectilecrosses twowalls ofequal height Hsymmetricallyas shown Q.70 ThetimeofflightTisgivenby (A) 8 s (B) 9 s (C) 7 s (D) 10 s Q.71 Theheightofeachwallis (A) 240 m (B) 120 m (C) 60 m (D) 30 m Q.72 Themaximumheightoftheprojectileis (A) 120 m (B) 80 m (C) 160 m (D) cannot be obtained Q.73 If the horizontal distance between thetwo walls is d = 120 m, then the range of the projectile is (A) 240 m (B) 160 m (C) 300 m (D) cannot be obtained Q.74 Theangleofprojectionof the projectile is (A) tan–1(3/4) (B) tan–1(4/3) (C) tan–1(4/5) (D) tan–1(3/5) Q.75 Thevelocityofprojectionis (A) 30 ms–1 (B) 40 ms–1 (C) 50 ms–1 (D) none of these Question No. 76 to 78 A projectileisthrown with avelocityof50 ms–1 atanangle of 53°with thehorizontal Q.76 Choose theincorrect statement (A)It travels verticallywith a velocityof40 ms–1 (B) It travelshorizontallywitha velocityof30 ms–1 (C)Theminimumvelocityoftheprojectileis30 ms–1 (D) None of these Q.77 Determinetheinstants at whichtheprojectileis at thesameheight (A) t = 1s and t = 7s (B) t = 3s and t = 5s (C) t = 2s and t = 6 s (D) all the above Q.78 Theequationofthe trajectoryis given by (A) 180y = 240x – x2 (B) 180y = x2 – 240x (C) 180y = 135x – x2 (D) 180y = x2 – 135x Question No. 79 & 80 At t = 0 a projectile is fired from a point O(taken as origin) on the ground witha speed of50m/s at an angleof53° with thehorizontal. It just passes two pointsA& B each at height 75 m above horizontal as shown. Q.79 Thehorizontal separationbetween the pointsAand B is (A) 30 m (B) 60 m (C) 90 m (D) None Q.80 Thedistance(in metres) of theparticlefrom origin at t = 2 sec. (A) 2 60 (B) 100 (C) 60 (D) 120
  13. Q.81 Aparticlestarts movingrectilinearlyattimet=0suchthatitsvelocity'v'changeswith time't'according to the equation v = t2 – t where t is in seconds and v is in m/s. The time interval for which the particle retards is (A) t < 1/2 (B) 1/2 < t < 1 (C) t > 1 (D) t < 1/2 and t > 1 Q.82 Aswimmer swims in still water at a speed =5 km/hr. He enters a 200 m wide river, having river flow speed = 4 km/hr at pointAand proceeds toswim at an angleof 127° (sin 37° = 0.6) with the river flow direction.AnotherpointBislocateddirectlyacrossAontheotherside.Theswimmerlandson theother bank at apoint C,from whichhe walks the distanceCBwith aspeed =3 km/hr.Thetotal timein which he reachrs fromAto B is (A)5minutes (B)4minutes (C)3minutes (D) None Q.83 Aboat havingaspeed of5km/hr. in still water,crosses a riverofwidth 1 km alongtheshortest possible path in 15minutes.The speed of the river in Km/hr. (A) 1 (B) 3 (C) 4 (D) 41 Q.84 Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity v and other with auniform acceleration a. If istheanglebetween thelinesofmotion oftwoparticles thentheleastvalue ofrelativevelocitywill beat timegiven by (A) (v/a)sin  (B) (v/a) cos  (C) (v/a) tan  (D) (v/a) cot  Q.85 Aflagis mounted on acarmovingdueNorth withvelocityof 20 km/hr. Strongwinds areblowingdue Eastwithvelocityof20km/hr.Theflagwillpointindirection (A) East (B) North - East (C) South - East (D) South - West Q.86 Amanis crossinga riverflowingwith velocityof5m/s. Hereachesapoint directlyacross at a distance of 60 m in 5 sec. His velocityin still water should be (A) 12 m/s (B) 13 m/s (C) 5 m/s (D) 10 m/s Q.87 AmanswimmingdownstreamovercomeafloatatapointM.AftertravellingdistanceDheturnedback and passed the float at a distance of D/2 from the point M, then the ratio of speed of swimmer with respect tostill waterto the speed of the river will be (A) 2 (B) 3 (C) 4 (D) 2.5 Q.88 Aglass wind screen whose inclination with the vertical can be changed is mounted on a car.The car moves horizontallywitha speed of 2m/s.At what angle  with the vertical should the wind screen be placed so that the rain drops fallingverticallydownwards with velocity 6 m/s strike the wind screen perpendicularly. (A) tan–1 (3) (B) tan–1 (1/3) (C) cos–1 (3) (D)sin–1 (1/3) Q.89 Wind is blowinginthenorth directionat speedof2m/s which causes therain to fall at someangle with the vertical.Withwhatvelocityshould acyclist driveso that therain appears vertical to him : (A) 2m/s south (B) 2m/s north (C) 4 m/s west (D) 4 m/s south Q.90 Three particles, locatedinitiallyon the vertices of an equilateral triangleof side L, start movingwith a constanttangential accelerationtowardseachotherinacyclicmanner, forming spiralloci thatcoverage at thecentroidof thetriangle. Thelengthofonesuchspirallocus will be (A) L/3 (B) 3 L 2 (C) 2 L (D) 2L/3
  14. Q.91 Find the speed of the intersection point O of the two wires if the wires starts movingperpendiculartoitselfwithspeedvasshowninfigure. (A) v cosec(/2) (B) v cosec() (C) v cos (/2) (D) v sec (/2) Q.92 At a given instant, A is moving with velocity of 5m/s upwards.What isvelocityof B at that time (A) 15 m/s  (B) 15 m/s  (C) 5 m/s  (D) 5 m/s  Q.93 Findthevelocityofthehangingblockifthevelocitiesof the free ends of the ropeare as indicated in the figure. (A) 3/2 m/s  (B) 3/2 m/s  (C) 1/2 m/s  (D) 1/2 m/s  Q.94 The pulleys in the diagram are all smooth and light.The acceleration ofAis a upwards and theacceleration of C is f downwards. The acceleration of B is (A) ½(f - a) up (B) ½(a + f) down (C) ½(a + f) up (D) ½(a - f) up Q.95 If acceleration of A is 2 m/s2 to left and acceleration of B is 1m/s2 toleft, then acceleration ofC is (A) 1 m/s2 upwards (B) 1 m/s2 downwards (C) 2 m/s2 downwards (D) 2 m/s2 upwards Q.96 The velocities of Aand Bare marked in the figure.The velocityof block C is (assumethat thepulleys areideal andstringinextensible) (A) 5 m/s (B) 2 m/s (C) 3 m/s (D) 4 m/s
  15. ONE OR MORE THAN ONE OPTION MAY BE CORRECT Take approx. 3 minutes for answering each question. Q.1 Aparticleis movingalongacurve.Then (A) if its speed is constant it has no acceleration (B)ifits speedis increasingtheacceleration oftheparticleis along itsdirection ofmotion (C)ifits speed is constantthe magnitude of itsacceleration is proportional to its curvature. (D)the directionof its acceleration cannot bealongthe tangent. Q.2 Ablockisthrownwith avelocityof2ms–1 (relativetoground)on abelt, which is movingwithvelocity 4 ms–1 in opposite direction of the initial velocityof block. If the block stops slipping on the belt after 4 sec of thethrowingthen choose the correct statements (s) (A)Displacementwithrespect togroundis zeroafter2.66and magnitudeof displacementwith respect to ground is 12 m after 4 sec. (B) Magnitude of displacement with respect to ground in 4 secis 4 m. (C) Magnitude of displacement with respect to belt in 4 sec is 12 m. (D) Displacement withrespect to ground is zero in 8/3 sec. Q.3 A particle has initial velocity10m/s.It movesdueto constant retardingforcealongthelineofvelocity which produces a retardation of 5 m/s2 .Then (A)themaximumdisplacementinthedirectionofinitialvelocityis10m (B) the distancetravelled in first 3 seconds is 7.5 m (C) the distancetravelled in first 3 seconds is 12.5 m (D) the distancetravelled in first 3 seconds is 17.5 m. Q.4 v-t graph of an object of mass 1 kg is shown (A) net work done on the object in 30 sec is zero. (B) theaverage acceleration of theobject is zero. (C) the average velocityof the object is zero. (D) the average force on the object is zero. Q.5 Velocity-time graphforacarissemicircle as shownhere.Whichofthe followingiscorrect: (A) Car mustmovein circularpath. (B)Acceleration of car is never zero. (C) Mean speed of the particle is /4 m/s. (D) The carmakes a turn onceduring its motion. Q.6 Mark thecorrect statements for aparticle going on astraight line (A) if thevelocityis zeroat anyinstant, the accelerationshould also be zero at that instant (B)ifthevelocityiszeroforatimeinterval,theaccelerationiszeroatanyinstantwithinthetimeinterval (C)ifthevelocityand accelerationhaveopposite sign, the object is slowing down (D)ifthepositionand velocityhave oppositesign, theparticleis movingtowardstheorigin Q.7 Fromthevelocitytimegarphofaparticlemovinginstraight linedecide whichofthefollowingisincorrectstatement. (A)the particlecrosses its initial position (B)thespeed of the particleincreases continuously (C) the force on the particle is constant (D) the acceleration of the particleis constant.
  16. Q.8 A particle initially at rest is subjected to two forces. One is constant, the other is a retarding force proportional totheparticle velocity. Inthesubsequent motion oftheparticle: (A)the accelerationwill increase from zero toa constant value (B)theaccelerationwill decreasefrom its initialvalue to zero (C)thevelocitywill increasefromzero tomaximum &thendecrease (D)the velocitywill increasefrom zero toa constant value. Q.9 Aparticlemoves in a circle of radius R, with a constant speed v.Then,during a time interval [R/3v], whichofthefollowingistrue? (A) | average acceleration | = 3v2/R (B) | average velocity| = 3v/ (C) | average acceleration | = 2v2/R (D) average speed = 3v/ Q.10 Anobservermoves withaconstantspeed alongthelinejoiningtwo stationaryobjects.Hewill observe that the two objects (A) have the same speed (B)havethe samevelocity (C) move inthe same direction (D)move inoppositedirections Q.11 Let v  and a  denote thevelocityand acceleration respectivelyof abodyin one–dimensional motion (A) | v |  must decrease when a  < 0 (B) Speed must increase when a  > 0 (C) Speed will increase when both v  and a  are < 0 (D) Speed will decrease when v  <0 and a  >0 Q.12 The figureshows thevelocity(v)ofaparticle plottedagainst time (t) (A) The particlechanges its directionofmotionat somepoint (B) Theaccelerationof theparticleremains constant (C)The displacement of the particleis zero (D)Theinitial and final speedsofthe particle arethesame Q.13 Whichofthefollowingstatements aretrue foramovingbody? (A)Ifits speedchanges, its velocitymust changeand it musthave someacceleration (B)Ifits velocitychanges, its speedmust changeand it musthave some acceleration (C) If its velocitychanges, its speedmayor maynot change, and it must have some acceleration (D)Ifits speed changes but direction of motion does not change, its velocitymayremain constant Q.14 Let v and a denote the velocityand acceleration respectivelyof a body (A) a can be non zero when v = 0 (B) a must be zero when v = 0 (C) a maybe zero when v  0 (D) The directionof amust havesome correlation with thedirection ofv Q.15 The displacement x of a particle depend on time t as x = t2 - t3 (A)particlewillreturn toits startingpointaftertime   . (B) the particlewill come to rest after time   3 2 (C)the initial velocityoftheparticle was zero butits initial acceleration wasnot zero. (D) no net force act on the particle at time   3
  17. Q.16 A projectile of mass 1 kg is projected witha velocityof 20 m/s suchthat it strikes on thesame level as the point of projection at adistance of 3 m. Which of the followingoptions are incorrect: (A) the maximum height reached bythe projectile can be 0.25 m. (B)theminimumvelocityduringits motioncanbe 15 m/s (C) the time taken for the flight can be 5 3 sec. (D)maximumpotentialenergyduringits motioncan be6J. Q.17 Choose the correct alternative (s) (A)Ifthegreatestheighttowhichaman canthrow astoneish,thenthegreatesthorizontal distanceupto which hecan throw the stone is 2h. (B) The angle of projection for a projectile motion whose range R is n times the maximum height is tan–1 (4/n) (C) The time of flight T and the horizontal range R of a projectile are connected by the equation gT2 = 2Rtan where  is theangle of projection. (D)Aball is thrown verticallyup.Another ball is thrown at an angle  with the vertical. Both of them remain in air for the same period of time. Then the ratio of heights attained bythe two balls 1 : 1. Q.18 Abeadis free toslidedown asmooth wiretightlystretched between pointsAand Bonavertical circle. If the beadstarts from rest atA, the highest point on the circle (A)its velocityvonarrivingat B is proportional to cos (B) its velocityv onarrivingat B is proportional to tan (C) time toarrive at B is proportional to cos (D) time toarrive at B is independent of  Q.19 IfTis thetotal timeofflight, histhemaximum height &R is therangefor horizontal motion, thex & y co-ordinates of projectile motion and time t arerelated as : (A) y = 4h t T t T              1 (B) y = 4h X R X R              1 (C) y = 4h T t T t              1 (D) y = 4h R X R X              1 Q.20 Amanonarectilinearlymovingcart,facingthedirectionofmotion,throwsaballstraightupwithrespect tohimself (A)Theballwillalways returntohim (B)Theballwillneverreturntohim (C)The ballwillreturntohimifthe cart moveswithconstant velocity (D)Theballwillfallbehindhimifthecartmoveswithsomeacceleration Q.21 Aparticlemoves inthexyplanewith aconstant acceleration'g'in thenegativey-direction. Its equation of motion is y= ax–bx2 , where a and b are constants. Which of the following are correct? (A) Thex-component ofits velocityis constant. (B)At theorigin, the y-component of its velocityis a b 2 g . (C)At theorigin, its velocitymakes an angle tan–1 (a)with thex-axis. (D) The particle moves exactlylikea projectile.
  18. Q.22 A ball is rolledoff alongtheedge of a horizontal table with velocity4 m/s. It hits theground after time 0.4 s.Which of the followingare correct? (A) The height of the table is 0.8 m (B) It hits the ground atan angle of 60° with the vertical (C) It covers a horizontal distance 1.6 m from the table (D)It hitstheground withverticalvelocity4m/s Q.23 Aparticleisprojected from theground with velocityu at angle withhorizontal. Thehorizontal range, maximum heightand timeofflight areR,HandTrespectively.Theyaregiven by, R = g 2 sin u2  , H = g 2 sin u 2 2  and T = g sin u 2  Now keeping u as fixed,  is varied from 30° to 60°. Then, (A)R will first increase then decrease,Hwill increase andT will decrease (B) R willfirst increasethen decreasewhileHandTboth will increase (C)R willdecrease whileH andT will increase (D)R willincreasewhileHandTwill increase Q.24 Aparticle moves with constant speed v along a regular hexagonABCDEF in the sameorder.Thenthe magnitudeoftheaveragevelocityforits motionfromAto (A) F is v/5 (B) D is v/3 (C) C is v3/2 (D) B is v
  19. ANSWER KEY ONLY ONE OPTION IS CORRECT. Q.1 C Q.2 C Q.3 C Q.4 B Q.5 B Q.6 B Q.7 C Q.8 B Q.9 B Q.10 A Q.11 D Q.12 D Q.13 C Q.14 A Q.15 B Q.16 B Q.17 D Q.18 C Q.19 C Q.20 B Q.21 C Q.22 B Q.23 B Q.24 A Q.25 A Q.26 C Q.27 B Q.28 C Q.29 A Q.30 B Q.31 C Q.32 B Q.33 B Q.34 D Q.35 A Q.36 C Q.37 B Q.38 C Q.39 A Q.40 A Q.41 A Q.42 B Q.43 C Q.44 C Q.45 C Q.46 B Q.47 C Q.48 C Q.49 C Q.50 B Q.51 C Q.52 C Q.53 D Q.54 B Q.55 D Q.56 C Q.57 C Q.58 D Q.59 A Q.60 D Q.61 D Q.62 D Q.63 A Q.64 B Q.65 B Q.66 B Q.67 C Q.68 D Q.69 B Q.70 A Q.71 C Q.72 B Q.73 A Q.74 B Q.75 C Q.76 A Q.77 D Q.78 A Q.79 B Q.80 A Q.81 B Q.82 B Q.83 B Q.84 B Q.85 C Q.86 B Q.87 B Q.88 A Q.89 B Q.90 D Q.91 A Q.92 A Q.93 A Q.94 A Q.95 A Q.96 A ONE OR MORE THAN ONE OPTION MAY BE CORRECT Q.1 C,D Q.2 B,C,D Q.3 A,C Q.4 A,B,D Q.5 C Q.6 B,C,D Q.7 B Q.8 B,D Q.9 A,B Q.10 A,B,C Q.11 C,D Q.12 A,B,C,D Q.13 A,C Q.14 A,C Q.15 A,B,C,D Q.16 D Q.17 A,B,C,D Q.18 A,D Q.19 A,B Q.20 C,D Q.21 A,B,C,D Q.22 A,C,D Q.23 B Q.24 A,C,D
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