STD XII Sci. - Shahjahanpedia
Useful for all Agricultural, Medical, Pharmacy and Engineering Entrance Examinationsheld across India.STD. XII Sci.Triumph PhysicsBased on Maharashtra Board SyllabusThird Edition: September 2014First Edition: July 2014Salient Features Exhaustive subtopic wise coverage of MCQs Important formulae provided in each chapter Hints included for relevant questions Various competitive exam questions updated till the latest year Includes solved MCQs from JEE (Main), AIPMT, CET 2014 Evaluation test provided at the end of each chapterSolutions/hints to Evaluation Test available in downloadable PDF format atwww. targetpublications.orgPrinted at: Jasmine Art Printers Pvt. Ltd. Navi MumbaiNo part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanicalincluding photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher.TEID : 765
Preface“Std. XII: Sci. Triumph Physics” is a complete and thorough guide to prepare students for a competitivelevel examination. The book will not only assist students with MCQs of Std. XII but will also help them to prepare forJEE, AIPMT, CET and various other competitive examinations.The content of this book is based on the Maharashtra State Board Syllabus. Formulae that form a vital part ofMCQ solving are provided in each chapter. Notes provide important information about the topic. Shortcuts provideeasy and less tedious solving methods. Mindbenders have been introduced to bridge the gap between a text booktopic and the student’s understanding of the same. A quick reference to the notes, shortcuts and mindbenders has beenprovided wherever possible.MCQs in each chapter are divided into three sections:Classical Thinking: consists of straight forward questions including knowledge based questions.Critical Thinking: consists of questions that require some understanding of the concept.Competitive Thinking: consists of questions from various competitive examinations like JEE, AIPMT, CET, CPMT etc.Hints have been provided to the MCQs which are broken down to the simplest form possible.An Evaluation Test has been provided at the end of each chapter to assess the level of preparation of thestudent on a competitive level.An additional feature called “The physics of .” has been included in the book to foster a keen interest inthe subject of physics.The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’venearly missed something or want to applaud us for our triumphs, we’d love to hear from you.Please write to us on : mail@targetpublications.orgBest of luck to all the aspirants!Yours faithfullyAuthorsSr.No.Topic NamePage No.Sr.No.Topic NamePage No.1Circular Motion111Interference and tational Motion9113Current agnetic Effects of ElectricCurrent6Surface Tension22315Magnetism5737Wave Motion25416Electromagnetic Induction5908Stationary Waves28917Electrons and Photons63918Atoms, Molecules andNuclei66519Semiconductors70520Communication Systems7379Kinetic Theory of Gases andRadiation33010Wave Theory of Light394
Target Publications Pvt. Ltd.01Chapter 01: Circular MotionCircular MotionSyllabus1.0Introduction1.1Angular ion between linear velocity andangular velocity1.4Uniform circular motion1.5Acceleration in U.C.M(Radial acceleration)1.6Centripetal and centrifugal forces1.7Banking of roads1.8Conical pendulum1.9Vertical circular motionandangularRiding on a vertical circular arc, this rollercoaster fans experience a net force andacceleration that point towards the centre of thecircle1.10 Kinematical equation for circular motion in analogy with linear motion1
Target Publications Pvt. Ltd.Std. XII : Triumph Physicsiii.Formulae1.a Uniform Circular Motion (U.C.M.):i.Instantaneous angular velocity, θv2π 2πn ω lim t 0rT tii.Average angular velocity,θ θ1 θ ωav 2 tt 2 t1where,θ1 angular position of the body at timet1θ2 angular position of the body at timet2iii. ω ωav for U.C.M.iv. If a particle makes n rotations in tsecond, then2πnωav tv.Angular acceleration α 0vi. Instantaneous angular acceleration, ωdωd 2θαinst lim 2 t 0 tdtdtvii. Average angular acceleration,ω ω1 ωαave. 2 tt 2 t1where, ω1 instantaneous angular speedat time t1ω2 instantaneous angular speed at timet2 .viii. Linear acceleration ix.x. Non-uniform circular motion:i.Radial component of acceleration,v2ar ω2r rii.Tangential component of acceleration,dvat dt2a 2r a 2t .(Magnitude only) v 2 dv r dt 2 iv.Relation between tangential and angularacceleration, 3. a T α r rαθ 0Centripetal force:i.ii.iii.mv2r mrω2 mvω mr (2πf)224π 2 mr 2π mr T2 T Magnitude of Centrifugal force, Magnitude of Centripetal forcemv2(in magnitude)i.e Fcf rWhen an electron moves round thenucleus of an atom along a circular path,we haveZe 2mv 2 mω2r24πε0 rrCentripetal force, Fcp 4π 2 rT2where, Z atomic number of thenucleus. m 4π2 n2r m4. centripetal acceleration ω vv24π2 r a vω rω2 4π2f2r rT212π Time period T ωfrequency (f )Relation between linear and angularvelocity: v ω r rω as θ 90 2.Net (linear) acceleration,Motion of a vehicle on a curve road:The maximum velocity v, with which avehicle can take a safe turn so that there is noskidding, is v µrgwhere, µ coefficient of limiting frictionbetween the wheels and the road.5.Banking of roads:The proper velocity or optimum v on a roadbanked by an angle θ with the horizontal isgiven by, µ tan θ rg s 1 µ s tan θ where r radius of curvature of roadg acceleration due to gravityµs coefficient of friction between road andtyreswhen µs 0, v rg tan θv
Target Publications Pvt. Ltd.6.Chapter 01: Circular MotionVertical Circular Motion:8.i.Velocity at highest point vH ii.Velocity at the lowest point vL iii.Velocity at a point along horizontal(midway position) vM 3rgrg5rgAcceleration at the highest point aH gAcceleration at the bottom point aL 5gAcceleration along horizontal aM 3gTension at top most point,mv 2B mg 0TH rviii. Tension at the lowest point,mv2A mg 6 mgTL rix. Tension at a point where the stringmakes an angle θ with the lower verticallineiv.v.vi.vii.Notes1.Radian measure must be used in equationsthat contain linear and angular quantities.2.Finite angular displacement is a scalarquantity because it does not obey the laws ofvector addition.3.In U.C.M., angular velocity ω is onlyxi.xii.7.mv2[ cos 90 0]TM rTotal energy at different points at thetop, bottom and horizontal,5EH EL EM mrg2Total energy at any point,1E mv 2 mgr(1 cos θ)2Conical Pendulum:i.Angular velocity,ii.a.ω gl cos θb.ω g tan θr2πl cos θ 2πPeriodic time ωg πiii. and angular displacement θ are variable vectors.4.All the points on a rotating body in U.C.M.have same ω except centre as it is notrotating.5.Instantaneous angular displacement is avector quantity.6.Angular speed is a scalar quantity but angularvelocity is a vector quantity but both havesame units i.e rad/s.7.The direction of θ , ω , α is given by the righthand thumb rule.8.The value of ω of earth about its axis is7 10 5 rad/s or 360 per day.9.When a particle moves in a circle withconstant speed, its velocity is variable becauseof changing direction.10.Circular motion is a two-dimensional motionin which the linear velocity and linearacceleration vectors lie in the plane of thecircle but the angular velocity and angularacceleration vectors are perpendicular to theplane of the circle.11.Centrifugal force is a fictitious force andholds good in a rotating frame of reference.l sin θg tan θRadius of horizontal circle,r l sin θ Tθ x. constant vector but angular acceleration α 2mv mg cos θrTension at midway position whereθ 90 (i.e. along horizontal)Kinematical equations in circular motion inanalog with linear motion:i.ω ω0 αt1 2αtii.θ ω0t 2iii. ω2 ω02 2 αθ 3
Target Publications Pvt. Ltd.12.An observer on the moving particleexperiences only the centrifugal force, but anobserver stationary with respect to the centrecan experience or measure only thecentripetal force.13.Whenever a particle is in a U.C.M. or nonU.C.M., centripetal and centrifugal forces actsimultaneously. They are both equal andopposite but do not cancel each other.14.Centripetal force and Centrifugal force arenot action-reaction forces as action-reactionforces act on different bodies.15.The direction of centripetal force is samewhether the rotation of the circular path isclockwise or anticlockwise.16.Centripetal force is not responsible forrotational motion of a body because onlytorque can produce rotational motion.17.Since the centripetal force acting on a particlein circular motion acts perpendicular to itsdisplacement (and also its velocity), the workdone by it is always zero.18.Centrifuge is an apparatus used to separateheavier particles from the lighter particles ina liquid.19.Range of acceleration in circular motion90 θ 180 .20.The radius of the curved path is the distancefrom the centre of curved path to the centre ofgravity of the body. It is to be consideredwhen the centre of gravity of body is at aheight from the surface of road or surface ofspherical body.21.Whenever a car is taking a horizontal turn, thenormal reaction is at the inner wheel.22.While taking a turn, when car overturns, itsinner wheels leave the ground first.23.For a vehicle negotiating a turn along acircular path, if its speed is very high, then thevehicle starts skidding outwards. This causesthe radius of the circle to increase resulting inthe decrease in the centripetal force.1[ Fcp ]T4Std. XII : Triumph Physics24.If a body moves in a cylindrical well (well ofdeath,) the velocity required will be minimumsafest velocity and in this case the weight ofthe body will be balanced by component ofnormal reaction and the minimum safestvelocity is given by the formulaµrg .25.Cyclist leans his cycle to make an angle toavoid topling; not to provide centripetal force.26.If a body is kept at rest at the highest point ofconvex road and pushed along the surface toperform circular motion, the body will fallrfromafter travelling a vertical distance of3the highest point where r is the radius of thecircular path.27.When a body moves in a circular path withconstant speed, its linear momentum changesat every point, but its kinetic energy remainsconstant.28.In horizontal uniform circular motion, kineticenergy and magnitude of linear momentumremains constant, but the direction of linearmomentum keeps on changing.29.Since the centripetal force is not zero for aparticle in circular motion, the torque acting is zero i.e., τ 0 (as the force is central)Hence the angular momentum is constant i.e. L constant.30.Whenever the body moves, the forceresponsible for motion is the vector sum of allthe forces acting at that point.For example, Lift going up and down withacceleration ‘a’.31.If a particle performing circular motion comes to rest momentarily, i.e. v 0, then it willmove along the radius towards the centre andif its radial acceleration is zero, i.e. ar 0,then the body will move along the tangentdrawn at that point.32.For non uniform circular motion a α r ω v
Target Publications Pvt. Ltd.33.When a bucket full of water is rotated in avertical circle, water will not spill only ifvelocity of bucket at the highest point is 34.Chapter 01: Circular Motion5.To find out number of revolutions, alwaysapply the formula,ωt 2πntθ ntNumber of revolutions 2π2π 2π6.Since Fc v , therefore, no work is done bythe centripetal force. [2π rad 360 1 rev.]7.Angle which, a cyclist should make with thevertical is the angle of banking along a curvedroad.8.On frictional surface, for a body performingcircular motion, the centripetal force isprovided by the force of friction.fS µN but on horizontal surface N mg9.The10.While rounding a curve on a level road,centripetal force required by the vehicle isprovided by force of friction between the tyresand the road.mv2 F µR µmgr11.To avoid dependence on friction for thesupply of necessary centripetal force, curvedroads are usually banked by raising outer edgeof the road above the inner edge.12.The angle of banking (θ) is given by,v2h tan θ 2rgl h2where h is height of the outer edge above theinner edge and l is length of the road.13.On the same basis, a cyclist has to bendthrough an angle θ from his vertical positionwhile rounding a curve of radius r withv2velocity v such that tan θ rggr .If velocity imparted to body at the lowestposition is equal to2rg , then it will oscillatein a semicircle.Mindbenders1.The maximum velocity with which a vehiclecan go without toppling, is given byv rgd 2hrg tan θd2hd distance between the wheelsh height of centre of gravity from the roadg acceleration due to gravitywhere, tan θ 2.3.Skidding of an object placed on a rotatingplatform:The maximum angular velocity of rotation ofthe platform so that object will not skid on it isωmax (µg / r)The angle made by the resultant accelerationwith the radius, a α tan 1 t a r Shortcuts1.The basic formula for acceleration is a ωv.2.In U.C.M., if central angle or angulardisplacement is given, then simply applyθdv 2v sin to determine change in velocity.23.There are two types of acceleration; ar (radial)and at (tangential) acceleration.dvFormula for ar ω2r and at or rαdt4.To calculate angular displacement, apply the1formula, θ ωt αt22 minimumsafe velocitygdroverturning is v 2hfornotIf θ is very very small, thenv2tan θ sin θ rgv2h rglwhere h is height of the outer edge from theinner edge and l is the distance between thetracks or width of the road.5
Target Publications Pvt. Ltd.14.Std. XII : Triumph PhysicsAlways remember the formulae for velocity ofthe body at the top, bottom and at the middleof a circle with two distinct cases:i.path is convexii.path is concaveRemember in both the cases, formula will bedifferent.19.The total energy of any body revolving in avertical circle is (5/2) mgr.20.The distance travelled by the particleperforming uniform circular motion in t2πrt.seconds is given by the formula, d T21.To find out any unknown quantity, if bodymoves in vertical circle, resolve mg and if thebody moves in horizontal circle, resolvetension or normal reaction.Remember if in the question, it is given thatbody falls from a certain point then at thatpoint N 0.22.Centripetal Force in Different Situations:Effect of rotation of earth about its axis:The apparent loss in weight of a body on itssurface mω2 R cos2 φ wherem mass of bodyω angular velocity of earthR radius of earthφ latitudei.A particle tied to a Tension in the stringstring and whirledin a horizontalcircleii.Vehicle taking a Frictionalforceturn on a level road exerted by the roadon the tyresmv2 mg N where N is normalri.reaction.mv2 N mgrii.15.16.In horizontal circle, tension will be equal tocentripetal force i.e. T i.The minimum velocity of projection atthe lowest point of vertical circle so thatthe string slacken at the highest point, isgiven by vL 18.5grvelocity at the highest point is vH ii.17.mv2rgrIf TL is the tension at the lowest point and THis the tension at the highest point thenTL TH 6 mgThe centripetalforceSituationiii. A vehicle onspeed breakera Weight of the body oracomponentofweightiv. Revolution of eartharound the sunv.Electron revolving Coulomb attractionaround the nucleus exertedbythein an atomprotons on electronsvi. A charged particle Magneticdescribinga exertedbycircular path in a magnetic fieldmagnetic fieldvii. Coin placed on diskWhenvL i.2gr , the body moves in a verticalsemicircle about the lowest point L,ii.vL iii.circular arc smaller than the semicircle.For a motor cyclist to loop a vertical2gr , then the body oscillates in aloop, vL 65gr and vH grGravitationalforceexerted by the sunforcetheIn this case frictionalforce gives necessarycentripetal force.viii. Car moving on a N sin θ givessmoothbanked necessary centripetalroadforce.ix. Passenger sitting ina turning carNecessary centripetalforce is provided byseat and passenger.
Target Publications Pvt. Ltd.Chapter 01: Circular MotionClassical Thinking1.11.2.Angular displacement is measured in(A) metre.(B) time.(C) radian.(D) steradian.3.A flywheel rotates at a constant speed of3000 r.p.m. The angle described by the shaftin one second is(A) 3 π rad(B) 30 π rad(C) 100 π rad(D) 3000 π rad4.5.An electric motor of 12 horse-power generatesan angular velocity of 125 rad/s. What will bethe frequency of rotation?(A) 20(B) 20/π(D) 40(C) 20/2π10.The ratio of angular speeds of seconds handand hour hand of a watch is(A) 1 : 720(B) 60 : 1(C) 1 : 60(D) 720 : 111.A body moves with constant angular velocityon a circle. Magnitude of angular accelerationis(A) rω2(B) constant(C) zero(D) rω12.A wheel having a diameter of 3 m starts fromrest and accelerates uniformly to an angularvelocity of 210 r.p.m. in 5 seconds. Angularacceleration of the wheel is(B) 3.3 rad s 2(A) 4.4 rad s 2 2(C) 2.2 rad s(D) 1.1 rad s 2Angular displacementThe angular displacement in circular motion is(A) dimensional quantity.(B) dimensionless quantity.(C) unitless and dimensionless quantity.(D) unitless quantity.1.29.Angularvelocityacceleration andangular Direction of α r is(A) tangent to path.(B) perpendicular to path.(C) parallel to the path.(D) along the path.1.313.Relation between linear velocity andangular velocity The vector relation between linear velocity v , angular velocity ω and radius vector r isgiven byWhat is the angular speed of the seconds handof a watch?(A) 60 rad/s(B) π rad/s(C) π/30 rad/s(D) 2 rad/s(A)(C) v ω rv ω. r(B)(D) v r ωv r ω14.A wheel has circumference C. If it makesf r.p.s., the linear speed of a point on thecircumference is(B) fC(A) 2πfC(C) fC/2π(D) fC/60A body of mass 100 g is revolving in ahorizontal circle. If its frequency of rotation is3.5 r.p.s. and radius of circular path is 0.5 m,the angular speed of the body is(A) 18 rad/s(B) 20 rad/s(C) 22 rad/s(D) 24 rad/s15.A body is whirled in a horizontal circle ofradius 20 cm. It has angular velocity of10 rad/s. What is its linear velocity at anypoint on circular path?(A) 10 m/s(B) 2 m/s(C) 20 m/s(D)2 m/sWhat is the angular velocity of the )rad/s(C)24640016.A particle moves in a circular path, 0.4 m inradius, with constant speed. If particle makes5 revolutions in each second of its motion, thespeed of the particle is(A) 10.6 m/s(B) 11.2 m/s(C) 12.6 m/s(D) 13.6 m/s6.The angular velocity of a particle rotating in acircular orbit 100 times per minute is(A) 1.66 rad/s(B) 10.47 rad/s(C) 10.47 deg/s(D) 60 deg/s7.8.7
Target Publications Pvt. Ltd.17.A particle P is moving in a circle of radius ′r′with a uniform speed v. C is the centre of thecircle and AB is a diameter. When passingthrough B, the angular velocity of P about Aand C are in the ratiov(A) 1 : 1(B) 1 : 2A C r B2r P(C) 2 : 1(D) 4 : 11.4Uniform Circular Motion (U.C.M.)18.In uniform circular motion,(A) both velocity and acceleration areconstant.(B) velocity changes and acceleration isconstant.(C) velocity is constant and accelerationchanges.(D) both velocity and acceleration change.19.A particle moves along a circular orbit withconstant angular velocity. This necessarilymeans,(A) its motion is confined to a single plane.(B) its motion is not confined to a singleplane.(C) nothing can be said regarding the planeof motion.(D) its motion is one-dimensional.20.21.22.Select the WRONG statement.(A) In U.C.M. linear speed is constant.(B) In U.C.M. linear velocity is constant.(C) In U.C.M. magnitude of angularmomentum is consta
“Std. XII: Sci. Triumph Physics” is a complete and thorough guide to prepare students for a competitive level examination. The book will not only assist students with MCQs of Std. XII but will also help them to prepare for JEE, AIPMT, CET and various other competitive examinations.
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Plate Plan It is recommended that a plate plan be designed before starting the assay. A plate plan template is provided on page 28. The following is a suggested plate plan: 123456789101112 A BB B Std 7 C Std 6 D Std 5 E Std 4 F Std 3 G Std 2 H Std 1 Std 7 Std 6 Std 5 Std 4 Std 3 Std 2 Std 1 B blank (Assay Diluent), Standards 7 through 1 .
Number of Clusters XII-9. C) Overlap XII-10. D) An Example XII-10. 5. Implementation XII-13. A) Storage Management XII-14. 6. Results XII-14. A) Clustering Costs XII-15. B) Effect of Document Ordering XII-19. Cl. Search Results on Clustered ADI Collection . XII-20. D) Search Results of Clustered Cranfield Collection. XII-31. 7. Conslusions XII .
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STANDARDS Military MIL-STD-481 MIL-STD-490 MIL-STD-681 MIL-STD-961 MIL-STD-1 174 MIL-STD-1267 MIL-STD-1 306 MIL-STD-1 464 DOD-STD-1 476 DOD-STD-1686 DOD-STD-2 167 MIL-STD-21 75 HANDBOOKS DOD-HDBK-263 Configuration Control - Engineering Changes, Deviations and Waivers (Short Form) Specificati
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Electromagnetic Interference: MIL- STD-461F Ballistic Shock: MIL-STD-810G Life Fire: MIL- STD-810G Explosive Environment: MIL -STD 810G Altitude to 60,000ft: MIL -STD 29595 Explosive Decompression: MIL- STD-810G Salt fog: MIL -STD 810G Sand and Dust requirements: MIL-STD-810G Extreme operating . environments . Commercial NATO
Rough paths, invariance principles in the rough path topology, additive functionals of Markov pro-cesses, Kipnis–Varadhan theory, homogenization, random conductance model, random walks with random conductances. We gratefully acknowledge financial support by the DFG via Research Unit FOR2402 — Rough paths, SPDEs and related topics. The main part of the work of T.O. was carried out while he .
