Written as per the revised syllabus prescribed by the Maharashtra State Board of Secondary and Higher Secondary Education, Pune.

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Letitia Thornton
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1 Witten as pe e evised syllabus pescibed by e Mahaashta State oad of Seconday and Highe Seconday Education, Pune. Pecise Physics I SD. XII Sci. Salient Featues Concise coveage of syllabus in Question nswe Fomat. Coves answes to all extual Questions and Intext Questions. Includes Solved and Pactice Numeicals. Includes making scheme fo oad Questions fom 2013 to Execise, Multiple Choice Questions and opic test at e end of each chapte fo effective pepaation. Pinted at: Repo Knowledgecast Ltd., Mumbai aget Publications Pvt. Ltd. No pat of is book may be epoduced o tansmitted in any fom o by any means, C.D. RM/udio Video Cassettes o electonic, mechanical including photocopying; ecoding o by any infomation stoage and etieval system wiout pemission in witing fom e Publishe. P.. No _12321_JUP

2 Contents S. No. Chapte Maks Page No. 1 Cicula Motion Gavitation Rotational Motion scillations Elasticity Suface ension Wave Motion Stationay Waves Kinetic heoy of Gases and Radiation oad Question Pape - Mach oad Question Pape - July oad Question Pape - Mach oad Question Pape - July Note: ll e extual questions ae epesented by * mak ll e Intext questions ae epesented by # mak

3 01 Cicula Motion Subtopics 1.0 Intoduction 1.1 ngula displacement 1.2 ngula velocity and angula acceleation 1.3 Relation between linea velocity and angula velocity 1.4 Unifom Cicula Motion 1.5 cceleation in U.C.M (Radial acceleation) 1.6 Centipetal and centifugal foces 1.0 Intoduction Q.1. Define cicula motion. Give its examples. ns: Definition: Motion of a paticle along e cicumfeence of a cicle is called cicula motion. Examples: i. he motion of a cyclist along a cicula pa. Motion of e moon aound e ea. i Motion of e ea aound e sun. iv. Motion of e tip of hands of a clock. v. Motion of electons aound e nucleus in an atom. 1.1 ngula displacement Q.2. What is adius vecto? ns: i. vecto dawn fom e cente of a cicle to position of a paticle on cicumfeence of cicle is called as adius vecto. It is given by, s = s whee, s = small linea distance = small angula displacement 1.7 anking of oads 1.8 Vetical cicula motion due to ea s gavitation 1.9 Equation fo velocity and enegy at diffeent positions in vetical cicula motion 1.10 Kinematical equations fo cicula motion in analogy wi linea motion i It is diected adially outwads. iv. Unit: mete (m) in SI system and centimete (cm) in CGS system. v. Dimensions: [M 0 L 1 0 ] Q.3. *Define angula displacement. Explain e tem angula displacement. ns: i. ngle taced by a adius vecto in a given time, at e cente of e cicula pa is called as angula displacement. Conside a paticle pefoming cicula motion in anticlockwise sense as shown in e figue. Let, = initial position of paticle at t = 0 Y = final position of paticle afte time t = angula displacement in time t = adius of e cicle s = leng of ac Y s 1

4 Std. XII Sci.: Pecise Physics - I i ngula displacement is given by, Leng of ac = adius of cicle = s iv. Unit: adian v. Diection of angula displacement is given by ight hand umb ule o ight handed scew ule. *Q.4. State ight hand umb ule to find e diection of angula displacement. ns: Right hand umb ule: Imagine e axis of otation to be held in ight hand wi e finges culed aound it and umb out-stetched. If e culed finges give e diection of motion of a paticle pefoming cicula motion en e diection of out-stetched umb gives e diection of angula displacement vecto. d *Q.5. Explain ight handed scew ule to find e diection of angula displacement. ns: i. Imagine e ight handed scew to be held in e place in which paticle is Diection of angula displacement pefoming cicula motion. If e ight handed scew is otated in e diection of paticle pefoming cicula motion en e diection in which scew tip advances, gives e diection of angula displacement. he tip of e scew advances in downwad diection, if sense of otation of e object is clockwise wheeas e tip of e scew advances in upwad diection, if sense of otation of e object is anticlockwise as shown in e figue. d Y Y Right handed scew ule ip of scew advancing in upwad diection #Q.6. e e following motions same o diffeent? i. Motion of tip of second hand of a clock. Motion of entie second hand of a clock. ns: o e motions ae diffeent. he tip of e second hand of a clock pefoms unifom cicula motion while e entie hand pefoms otational motion wi e second hand as a igid body. 1.2 ngula velocity and angula acceleation Q.7. *Define angula velocity. What is angula velocity? State its unit and dimension. ns: i. ngula velocity of a paticle pefoming cicula motion is defined as e time ate of change of limiting angula displacement. he atio of angula displacement to time is called angula velocity. It is denoted by Instantaneous angula velocity is given by, = lim = d t 0 t Finite angula velocity is given by, = t Q.8. *Define angula acceleation. What is angula acceleation? State its unit and dimension. ns: i. he ate of change of angula velocity wi espect to time is called angula acceleation. It is denoted by. If 0 and ae e angula velocities of a paticle pefoming cicula motion at instant t 0 and t, en angula acceleation is given by, 0 = = t t 0 t 2

5 i iv. It is a vecto quantity. Diection: he diection of angula velocity is given by ight hand ule and is in e diection of angula displacement. v. Unit: ad s 1 vi. Dimensions: [M 0 L 0 1 ] i It is a vecto quantity Chapte 01: Cicula Motion iv. Diection: he diection of is given by ight hand umb ule o ight handed scew ule. v. Unit: ad /s 2 in SI system. vi. Dimensions: [M 0 L 0 2 ]. Q.9. Define i. veage angula acceleation Instantaneous angula acceleation ns: i. veage angula acceleation: Instantaneous angula acceleation: veage angula acceleation is defined as e time ate of change of angula velocity. Instantaneous angula acceleation is defined as e limiting ate of change of angula velocity. 2 1 It is given by avg = = It is given by = lim t t t t 0 t 2 1 Solved Examples Q.10. What is e angula displacement of second hand in 5 seconds? Given: = 60 s, t = 5 s o find: ngula displacement () Fomula: = 2 t Calculation: Fom fomula, = = ad ns: he angula displacement of second hand in 5 seconds is ad. Q.11. Calculate e angula velocity of ea due to its spin motion. Given: = 24 hou = s o find: ngula velocity () Fomula: = 2 Calculation: Fom fomula, 2 = = = ad/s ns: he angula velocity of ea due to its spin motion is ad/s. 1.3 Relation between linea velocity and angula velocity Q.12. Define linea velocity. *Show at linea speed of a paticle pefoming cicula motion is e poduct of adius of cicle and angula speed of paticle. ns: Linea velocity: Distance tavelled by a body pe unit time in a given diection is called linea velocity. It is a vecto quantity and is given by, ds v = Relation between linea velocity and angula velocity: i. Conside a paticle moving wi unifom cicula motion along e cicumfeence of a cicle in anticlockwise diection wi cente and adius as shown in e figue. v s v Let e paticle cove small distance s fom to in small inteval t. In such case, small angula displacement is =. 3

6 Std. XII Sci.: Pecise Physics - I 4 i Magnitude of instantaneous linea velocity of paticle is given by, s v = lim δt0 t ut s = v = lim t 0 t [ = constant] lso lim t 0 t v = In vecto fom, v = Q.13. *Pove e elation v =, whee symbols have ei usual meaning. In U.C.M. (Unifom Cicula Motion), pove e elation v, whee symbols have ei usual meanings. [Ma 16] ns: nalytical meod: i. Conside a paticle pefoming cicula motion in anticlockwise sense wi cente and adius as shown in e figue. Let, = angula velocity of e paticle v = linea velocity of e paticle = adius vecto of e paticle [Diagam - ½ Mak] i Linea displacement in vecto fom is given by, s = [½ Mak] Dividing bo side by t, s t = t.(1) iv. aking limiting value in equation (1) s lim = lim t 0 t t 0 t ds = d [½ Mak] v ut, ds = v = linea velocity, d = = angula velocity v = [**Explanation ½ Mak] Calculus meod: i. paticle is moving in XY plane wi position vecto, = îcos t + ĵsin t.(1) ngula velocity is diected pependicula to plane, i.e., along i Solved Examples Z-axis. It is given by = ˆk, whee, ˆk = unit vecto along Z-axis. = ˆk ( îcos t + ĵ sin t) [Fom equation (1)] = cos t ( ˆk î) + sin t ( ˆk ĵ) = ĵ cos t + ( î) sin t ki j and k ji = î sin t + ĵ cos t = ( îsin t + ĵ cos t). (2) lso v = d ˆ isintˆjcos t v = ˆisintˆjcos t.(3) Fom equation (2) and (3), v = = *Q.14.Calculate e angula velocity and linea velocity of a tip of minute hand of leng 10 cm. Given: = 60 min. = s = 3600 s, l = 10 cm = 0.1 m o find: i. ngula velocity () Linea velocity (v) Fomulae: i. = 2 v =

7 Chapte 01: Cicula Motion Calculation: Fom fomula (i), = 2 = = ad/s Fom fomula (ii), v = = v = m/s ns: he tip of e minute hand has angula velocity ad/s and linea velocity m/s. Q.15. n aicaft takes a tun along a cicula pa of adius 1500 m. If e linea speed of e aicaft is 300 m/s, find its angula speed and time taken by it to complete 1 5 of cicula pa. Given: = 1500 m, v = 300 m/s o find: i. ngula speed () 1 ime taken fo of cicula 5 pa (t) Fomulae: i. v = = t Calculation: Fom fomula (i), = v = = = 1 5 = 0.2 ad/s he angula displacement () of e 1 aicaft to complete of e 5 cicula pa is = 2 ad 5 Fom fomula (ii), t = = 2 /5 0.2 t = = s ns: he angula speed of e aicaft is 0.2 ad/s 1 and time taken by it to complete 5 of cicula pa is s. 1.4 Unifom Cicula Motion Q.16. *Define unifom cicula motion. Explain e tem unifom cicula motion. ns: i. he motion of a body along e cicumfeence of a cicle wi constant speed is called unifom cicula motion. In U.C.M, diection of velocity is along e tangent dawn to e position of paticle on cicumfeence of e cicle. i Hence, diection of velocity goes on changing continuously, howeve e magnitude of velocity is constant. heefoe, magnitude of angula velocity is constant. iv. Examples of U.C.M: a. Motion of e ea aound e sun. b. Motion of e moon aound e ea. c. Revolution of electon aound e nucleus of atom. Q.17. State e chaacteistics of unifom cicula motion. ns: Chaacteistics of U.C.M: i. It is a peiodic motion wi definite peiod and fequency. Speed of paticle emains constant but velocity changes continuously. i iv. It is an acceleated motion. Wok done in one peiod of U.C.M is zeo. Q.18. Define peiodic motion. Why U.C.M is called peiodic motion? ns: i. Definition: type of motion which is epeated afte equal inteval of time is called peiodic motion. he paticle pefoming U.C.M epeats its motion afte equal intevals of time on e same pa. Hence, U.C.M is called peiodic motion. 5

6.4 Period and Frequency for Uniform Circular Motion

6.4 Period and Frequency for Uniform Circular Motion 6.4 Peiod and Fequency fo Unifom Cicula Motion If the object is constained to move in a cicle and the total tangential foce acting on the total object is zeo, F θ = 0, then (Newton s Second Law), the tangential