CLASS

X

LEE SHE KALYAN DHARMENDRA PANT

CERTIFICATE

PHYSICS

+PCEEQTFCPEGYKVJVJGNCVGUVU[NNCDWURTGUETKDGFD[VJG%QWPEKNHQTVJG+PFKCP%GTVKſECVGQH Secondary Education Examination, New Delhi.

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PHYSICS Class X Edition-Coordinator

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(M.Sc., B.Ed.) Department of Physics Don Bosco School, 6LOLJXUL

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M.Sc. (Honors); M.Ed. H.O.D. Physics St. Xavier's Senior Secondary School, &KDQGLJDUK

OSWAL PUBLISHERS

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PREFACE Physics is a branch of science that deals with the study of mechanics of naturally occurring phenomenon, such as the interactions of matter and energy. Its study involves experiments with qualitative as well as quantitative measures. 9KVJ KOOGPUG RNGCUWTG YG RTGUGPV VJG 6GZVDQQM QH %GTVKſECVG 2J[UKEU YJKEJ JCU DGGP FGUKIPGF KP CEEQTFCPEGYKVJVJGNCVGUVU[NNCDWUHQTENCUU:CURTGUETKDGFD[VJG%QWPEKNHQTVJG+PFKCP5EJQQN%GTVKſECVG Examination (ICSE). The main objective of writing this book is to present the subject matter at an elementary level with an interesting approach. 6JGVGZVDQQMEQXGTUVJGVJGQTGVKECNRTCEVKECNCPFCRRNKGFCURGEVUQHGCEJEJCRVGTKPCUKORNKſGFOCPPGT Several illustrations have been included in each chapter for a better understanding of the subject. In the beginning of each chapter, a ‘Learning path’ has been incorporated, which broadly highlights the topics covered in the chapter. There is a ‘Do you know?’ section in every chapter, which states certain interesting facts which would DGHCUEKPCVKPIHQTVJGUVWFGPVU&GſPKVKQPUNCYUCPFKORQTVCPVVGTOUJCXGDGGPGORJCUK\GFD[WUKPIVJG+VCNKEU and Bold format. Examples and note points have been placed in a particular layout to make them stand out. 6JGTGCTGCPWODGTQHUQNXGFGZCORNGUCNQPIYKVJVJGGZGTEKUGUGEVKQPVJCVCKFUKPCPCN[\KPIVJGGPVKTG content of the section. The exercise section includes multiple choice questions, short and long answer type questions and numerical problems for the students’ practice. Hints and solutions have been provided for selective questions. Questions from a few previous years’ examination papers have also been included in each chapter for students to understand the pattern of the questions asked in the board examination. Sincere thanks to all the teachers who have provided their valuable feedback for this text book. We would like to express our gratitude towards ‘Oswal Publishers’ for their co-operation, guidance and assistance in bringing out this book to our entire satisfaction. Suggestions and feedback from all readers for the further improvement of this book in its subsequent editions are welcome. Authors

SYLLABUS CLASS - X KHDWQXFOHDUOLJKWDQGVRXQGHQHUJ\FRQYHUVLRQIURP 7KHUHZLOOEHRQHSDSHURIWZRKRXUVGXUDWLRQFDUU\LQJ RQHIRUPWRDQRWKHUFRPPRQH[DPSOHV PDUNVDQG,QWHUQDO$VVHVVPHQWRISUDFWLFDOZRUNFDUU\LQJ PDUNV (v) Machines as force multipliers; load, effort, mechanical advantage, velocity ratio and 7KH SDSHU ZLOO EH GLYLGHG LQWR WZR VHFWLRQV 6HFWLRQ ,  GHſEKGPE[ UKORNG VTGCVOGPV QH NGXGTU RWNNG[ PDUNV DQG6HFWLRQ,,PDUNV  systems showing the utility of each type of Section I FRPSXOVRU\ ZLOOFRQWDLQVKRUWDQVZHUTXHVWLRQV machine. RQWKHHQWLUHV\OODEXV )XQFWLRQV DQG XVHV RI VLPSOH PDFKLQHV  7HUPVă Section II ZLOO FRQWDLQ VL[ TXHVWLRQV &DQGLGDWHV ZLOO EH HIIRUW ( ORDG / PHFKDQLFDO DGYDQWDJH 0$  /( UHTXLUHGWRDQVZHUDQ\IRXURIWKHVHVL[TXHVWLRQV YHORFLW\UDWLR95 9(9/ G(G/LQSXW:L RXWSXW Note 8QOHVVRWKHUZLVHVSHFLILHGRQO\6,8QLWVDUHWREH :R  HIILFLHQF\ K  UHODWLRQ EHWZHHQ K DQG 0$95 XVHGZKLOHWHDFKLQJDQGOHDUQLQJDVZHOODVIRUDQVZHULQJ GHULYDWLRQLQFOXGHG IRUDOOSUDFWLFDOPDFKLQHVK TXHVWLRQV 0$95 1. Force, Work, Power and Energy  /HYHUSULQFLSOH)LUVWVHFRQGDQGWKLUGFODVVRIOHYHUV H[DPSOHV0$DQG95LQHDFKFDVH([DPSOHVRIHDFK (i) Turning forces concept; moment of a force; forces RI WKHVH FODVVHV RI OHYHUV DV DOVR IRXQG LQ WKH KXPDQ in equilibrium; centre of gravity; [discussions ERG\ using simple examples and simple numerical problems].  3XOOH\V\VWHPVLQJOHIL[HGVLQJOHPRYDEOHEORFNDQG WDFNOH0$95DQGKLQHDFKFDVH (OHPHQWDU\LQWURGXFWLRQRIWUDQVODWLRQDODQGURWDWLRQDO PRWLRQVPRPHQWWXUQLQJHIIHFW RIDIRUFHDOVRFDOOHG (vi) Principle of Conservation of energy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ight RI JUDYLW\ TXDOLWDWLYH RQO\  ZLWK H[DPSOHV RI VRPH (i) Refraction of light through a glass block and a UHJXODUERGLHVDQGLUUHJXODUODPLQD triangular prism - qualitative treatment of simple (ii) Uniform circular motion. applications such as real and apparent depth of $V DQ H[DPSOH RI FRQVWDQW VSHHG WKRXJK DFFHOHUDWLRQ objects in water and apparent bending of sticks in IRUFH LVSUHVHQW'LIIHUHQFHVEHWZHHQFHQWULIXJDODQG water. Applications of refraction of light. FHQWULSHWDOIRUFH 3DUWLDO UHIOHFWLRQ DQG UHIUDFWLRQ GXH WR FKDQJH LQ (iii) Work, energy, power and their relation with PHGLXP /DZV RI UHIUDFWLRQ WKH HIIHFW RQ VSHHG force. 9  ZDYHOHQJWK O  DQG IUHTXHQF\ I  GXH WR UHIUDFWLRQ RI OLJKW FRQGLWLRQV IRU D OLJKW UD\ WR SDVV 'HILQLWLRQ RI ZRUN :  )6FRVT VSHFLDO FDVHV RI XQGHYLDWHG 9DOXHV RI VSHHG RI OLJKW F  LQ YDFXXP T  °Ĉ °Ĉ :  PJK 'HILQLWLRQ RI HQHUJ\ HQHUJ\ DLU ZDWHU DQG JODVV UHIUDFWLYH LQGH[ —  F9 DV ZRUN GRQH 9DULRXV XQLWV RI ZRUN DQG HQHUJ\ DQG 9  IO 9DOXHV RI — IRU FRPPRQ VXEVWDQFHV VXFK DV WKHLUUHODWLRQZLWK6,XQLWV>HUJFDORULHN:KDQGH9@ ZDWHU JODVV DQG GLDPRQG H[SHULPHQWDO YHULILFDWLRQ 'HILQLWLRQ RI 3RZHU 3 :W 6, DQG FJV XQLWV RWKHU UHIUDFWLRQ WKURXJK JODVV EORFN ODWHUDO GLVSODFHPHQW XQLWV NLORZDWW N:  PHJDZDWW 0:  DQG JLJDZDWW PXOWLSOHLPDJHVLQWKLFNJODVVSODWHPLUURUUHIUDFWLRQ *:  DQG KRUVH SRZHU  KS   :  >6LPSOH WKURXJK D JODVV SULVP VLPSOH DSSOLFDWLRQV  UHDO DQG QXPHULFDOSUREOHPVRQZRUNSRZHUDQGHQHUJ\@ DSSDUHQWGHSWKRIREMHFWVLQZDWHUDSSDUHQWEHQGLQJRI (iv) Different types of energy (e.g. chemical energy, D VWLFN XQGHU ZDWHU 6LPSOH QXPHULFDO SUREOHPV DQG Mechanical energy, heat energy, electrical energy, DSSUR[LPDWHUD\GLDJUDPVUHTXLUHG  nuclear energy, sound energy, light energy). 0HFKDQLFDO HQHUJ\ SRWHQWLDO HQHUJ\ 8  PJK KK 6QVCN KPVGTPCN TGƀGEVKQP %TKVKECN CPING GZCORNGU in triangular glass prisms; comparison with GHULYDWLRQ LQFOXGHG  JUDYLWDWLRQDO 3( H[DPSOHV  TGƀGEVKQP HTQO C RNCPG OKTTQT SWCNKVCVKXG QPN[ NLQHWLF HQHUJ\ .  ó PY  GHULYDWLRQ LQFOXGHG  #RRNKECVKQPUQHVQVCNKPVGTPCNTGƀGEVKQP IRUPV RI NLQHWLF HQHUJ\ WUDQVODWLRQDO URWDWLRQDO DQG YLEUDWLRQDO  RQO\ VLPSOH H[DPSOHV >1XPHULFDO 7UDQVPLVVLRQ RI OLJKW IURP D GHQVHU PHGLXP JODVV SUREOHPV RQ . DQG 8 RQO\ LQ FDVH RI WUDQVODWLRQDO ZDWHU  WR D UDUHU PHGLXP DLU  DW GLIIHUHQW DQJOHV RI PRWLRQ@TXDOLWDWLYHGLVFXVVLRQVRIHOHFWULFDOFKHPLFDO LQFLGHQFH FULWLFDO DQJOH &  —  VLQ & (VVHQWLDO

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(iii) Loudness, pitch and quality of sound :  &KDUDFWHULVWLFV RI VRXQG ORXGQHVV DQG LQWHQVLW\ VXEMHFWLYH DQG REMHFWLYH QDWXUH RI WKHVH SURSHUWLHV VRXQG OHYHO LQ GE DV XQLW RQO\  QRLVH SROOXWLRQ LQWHUGHSHQGHQFH RI  SLWFK DQG IUHTXHQF\ TXDOLW\ DQG ZDYHIRUPVZLWKH[DPSOHV  4. Electricity and Magnetism (i) Ohm’s Law; concepts of emf, potential difference, resistance; resistances in series and parallel, internal resistance. &RQFHSWV RI SG 9  FXUUHQW ,  UHVLVWDQFH 5  DQG FKDUJH 4  2KP V ODZ VWDWHPHQW 9  ,5 6, XQLWV H[SHULPHQWDOYHULILFDWLRQJUDSKRI9YV,DQGUHVLVWDQFH IURP VORSH RKPLF DQG QRQRKPLF UHVLVWRUV IDFWRUV DIIHFWLQJUHVLVWDQFHLQFOXGLQJVSHFLILFUHVLVWDQFH DQG LQWHUQDO UHVLVWDQFH VXSHU FRQGXFWRUV HOHFWURPRWLYH IRUFH HPI  FRPELQDWLRQ RI UHVLVWDQFHV LQ VHULHV DQG SDUDOOHO DQG GHULYDWLRQ RI H[SUHVVLRQV IRU HTXLYDOHQW UHVLVWDQFH6LPSOHQXPHULFDOSUREOHPVXVLQJWKHDERYH UHODWLRQV>6LPSOHQHWZRUNRIUHVLVWRUV@ (ii) Electrical power and energy. (OHFWULFDO HQHUJ\ H[DPSOHV RI KHDWHU PRWRU ODPS ORXGVSHDNHU HWF (OHFWULFDO SRZHU PHDVXUHPHQW RI HOHFWULFDO HQHUJ\ :  49  9,W IURP WKH GHILQLWLRQ RISG&RPELQLQJZLWKRKP¶VODZ: 9,W ,5W  95 WDQGHOHFWULFDOSRZHU3 :W  9, ,5  95 8QLWV  6, DQG FRPPHUFLDO 3RZHU UDWLQJ RI FRPPRQDSSOLDQFHVKRXVHKROGFRQVXPSWLRQRIHOHFWULF HQHUJ\ FDOFXODWLRQ RI WRWDO HQHUJ\ FRQVXPHG E\ HOHFWULFDO DSSOLDQFHV :  3W NLORZDWW × KRXU  N: K >VLPSOHQXPHULFDOSUREOHPV@ (iii) Household circuits – main circuit; switches; fuses; earthing; safety precautions; three-pin plugs; colour coding of wires. +RXVHZLULQJULQJV\VWHP SRZHUGLVWULEXWLRQPDLQ FLUFXLWZLUHVOLYHQHXWUDOHDUWK ZLWKIXVH0&% PDLQ VZLWFK DQG LWV DGYDQWDJHV ă FLUFXLW GLDJUDP WZRZD\ VZLWFK VWDLUFDVH ZLULQJ QHHG IRU HDUWKLQJ IXVH SLQ SOXJ DQG VRFNHW &RQYHQWLRQDO ORFDWLRQ RI OLYH QHXWUDO DQG HDUWK SRLQWV LQ  SLQ SOXJV DQG VRFNHWV6DIHW\SUHFDXWLRQVFRORXUFRGLQJRIZLUHV (iv) Magnetic effect of a current (principles only, laws not required); electromagnetic induction (elementary); transformer. 2HUVWHG¶VH[SHULPHQWRQWKHPDJQHWLFHIIHFWRIHOHFWULF FXUUHQW PDJQHWLF ILHOG %  DQG ILHOG OLQHV GXH WR FXUUHQW LQ D VWUDLJKW ZLUH TXDOLWDWLYH RQO\  ULJKW KDQGWKXPEUXOHăPDJQHWLFILHOGGXHWRDFXUUHQWLQ D ORRS (OHFWURPDJQHWV WKHLU XVHV FRPSDULVRQV ZLWK D SHUPDQHQW PDJQHW )OHPLQJ¶V /HIW +DQG 5XOH WKH '& HOHFWULF PRWRU VLPSOH VNHWFK RI PDLQ SDUWV FRLO PDJQHW VSOLW ULQJ FRPPXWDWRUV DQG EUXVKHV  EULHI GHVFULSWLRQ DQG W\SH RI HQHUJ\ WUDQVIHUZRUNLQJ QRW UHTXLUHG  6LPSOH LQWURGXFWLRQ WR HOHFWURPDJQHWLF

LQGXFWLRQ IUHTXHQF\ RI $& LQ KRXVH KROG VXSSOLHV  Fundamental units )OHPLQJ¶V 5LJKW +DQG 5XOH $& *HQHUDWRU ă 6LPSOH The system has seven fundamental (or basic) units, VNHWFK RI PDLQ SDUWV EULHI GHVFULSWLRQ DQG W\SH RI one for each of the fundamental quantities. HQHUJ\ WUDQVIHUZRUNLQJ QRW UHTXLUHG  $GYDQWDJH RI Unit Fundamental quantity $& RYHU '& 7UDQVIRUPHU LWV W\SHV FKDUDFWHULVWLFV Name Symbol RI SULPDU\ DQG VHFRQGDU\ FRLOV LQ HDFK W\SH VLPSOH Mass kilogram kg ODEHOOHGGLDJUDPDQGLWVXVHV  Length metre m 5. Heat Time second s

K %CNQTKOGVT[ OGCPKPI URGEKſE JGCV ECRCEKV[ Electric current ampere A principle of method of mixtures; Numerical kelvin K 2TQDNGOUQPURGEKſEJGCVECRCEKV[WUKPIJGCVNQUU Temperature Luminous intensity candela cd and gain and the method of mixtures. mole mol +HDW DQG LWV XQLWV FDORULH MRXOH  WHPSHUDWXUH DQG Amount of substance LWVXQLWV°&. WKHUPDOKHDW FDSDFLW\&  4'7 Derived units 6,XQLWRI& 6SHFLILFKHDW&DSDFLW\& 4P'76, These are obtained from the fundamental units by XQLWRI& 0XWXDOUHODWLRQEHWZHHQ+HDW&DSDFLW\DQG multiplication or division; no numerical factors are 6SHFLILF +HDW FDSDFLW\ YDOXHV RI & IRU VRPH FRPPRQ involved. Some derived units with complex names VXEVWDQFHVLFHZDWHUDQGFRSSHU 3ULQFLSOHRIPHWKRG are : RIPL[WXUHVLQFOXGLQJPDWKHPDWLFDOVWDWHPHQW1DWXUDO Unit Derived SKHQRPHQRQ LQYROYLQJ VSHFLILF KHDW &RQVHTXHQFHV RI quantity Name Symbol KLJKVSKHDWRIZDWHU>6LPSOHQXPHULFDOSUREOHP@ Volume cubic metre m3 (ii) Latent heat; loss and gain of heat involving Density kilogram per cubic kg.m–3 change of state for fusion only. metre Change of phase (state); heating curve for water; Velocity metre per second m. s–1 latent heat; sp latent heat of fusion (SI unit). Acceleration metre per second m. s–2 Simple numerical problems. Common physical squared phenomena involving latent heat of fusion. Momentum kilogram metre per kg.m. s–1 second 6. Modern Physics (i) Radioactivity and changes in the nucleus; Some derived units are given special names due to their complexity when expressed in terms of the background radiation and safety precautions. fundamental units, as below : %ULHI LQWURGXFWLRQ TXDOLWDWLYH RQO\  RI WKH QXFOHXV Unit Derived QXFOHDU VWUXFWXUH DWRPLF QXPEHU =  PDVV QXPEHU quantity Name Symbol $ 5DGLRDFWLYLW\ DV VSRQWDQHRXV GLVLQWHJUDWLRQ D E DQG J ă WKHLU QDWXUH DQG SURSHUWLHV FKDQJHV ZLWKLQ Force newton N WKH QXFOHXV 2QH H[DPSOH HDFK RI D DQG E GHFD\ Pressure pascal Pa ZLWKHTXDWLRQVVKRZLQJFKDQJHVLQ=DQG$8VHVRI Energy, Work joule J UDGLRDFWLYLW\ ă UDGLR LVRWRSHV +DUPIXO HIIHFWV 6DIHW\ Power watt W SUHFDXWLRQV%DFNJURXQGUDGLDWLRQ JGTV\ *\  5DGLDWLRQ  ;UD\V UDGLRDFWLYH IDOORXW IURP QXFOHDU Frequency Electric charge coulomb C SODQWVDQGRWKHUVRXUFHV : ohm  1XFOHDU (QHUJ\ ZRUNLQJ RQ VDIH GLVSRVDO RI ZDVWH Electric resistance Electromotive 6DIHW\PHDVXUHVWREHVWULFWO\UHLQIRUFHG volt V (ii) 1XFOHDU ILVVLRQ DQG IXVLRQ EDVLF LQWURGXFWLRQ DQG force When the unit is named after a person, the symbol HTXDWLRQV has a capital letter. 5VCPFCTFRTGſZGU A NOTE ON SI UNITS SI units (6\VWHPH ,QWHUQDWLRQDO G¶8QLWHV) were adopted Decimal multiples and submultiples are attached to units when appropriate, as below : internationally in 1968.

Multiple 109 106 103 10–1 10–2 10–3 10–6 10–9 10–12 10–15

2TGſZ giga mega kilo deci centi milli micro nano pico femto

Symbol G M k d c m μ n p f

INTERNAL ASSESSMENT OF PRACTICAL WORK

Candidates will be asked to carry out experiments for which instructions will be given. The experiments may be based on topics that are not included in the syllabus but theoretical knowledge will not be required. A candidate will be expected to be able to follow simple instructions, to take suitable readings and to present these readings in a systematic form. He/she may be required to exhibit his/her data graphically. Candidates will be expected to appreciate CPFWUGVJGEQPEGRVUQHNGCUVEQWPVUKIPKſECPVſIWTGU and elementary error handling. Note : Teachers may design their own set of experiments, preferably related to the theory syllabus. A comprehensive list is suggested below. 1. Lever : There are many possibilities with a meter rule as a lever with a load (known or unknown) suspended from a point near one end (say left), the lever itself pivoted on a knife edge, use slotted weights suspended from the other (right) side for effort. Determine the mass of a metre rule using a spring balance or by balancing it on a knife edge at some point away from the middle and a 50 g weight on the other side. Next pivot (F) the metre rule at the 40 cm, 50 cm and 60 cm mark, each time suspending a load L or the left end and effort E near the right end. Adjust E and or its position so that the rule is balanced. Tabulate the position of L, F and E and the magnitudes of L and E and the distances of load arm and effort arm. Calculate MA = L/E and VR = effort arm/ load arm. It will be found that MA VR in the third case. Try to explain why this is so. Also try to calculate the real load and real effort in these cases. 2. Determine the VR and MA of a given pulley system.

3.

Trace the course of different rays of light refracting through a rectangular glass slab at different angles of incidence, measure the angles of incidence, refraction and emergence. Also measure the lateral displacement. 4. Determine the focal length of a convex lens by (a) the distant object method and (b) using a needle and a plane mirror. 5. Determine the focal length of a convex lens by using two pins and formula I = XY/(X + Y). 6. For a triangular prism, trace the course of rays passing through it, measure angles L1, L2, A and G. Repeat for four different angles of incidence (say L1 = 40°, 50°, 60° and 70°). Verify L1+ L2 = A + G and A = U1 + U2 . 7. For a ray of light incident normally (L1 = 0) on one face of a prism, trace course of the ray. Measure the angle G 'ZRNCKP DTKGƀ[ &Q VJKU HQT RTKUOU with A = 60°, 45° and 90°. 8. Calculate the sp. heat of the material of the given calorimeter, from the temperature readings and masses of cold water, warm water and its mixture taken in the calorimeter. 9. Determination of sp. heat of a metal by method of mixtures.  &GVGTOKPCVKQPQHURGEKſENCVGPVJGCVQHKEG 11. Using a simple electric circuit, verify Ohm’s law. Draw a graph, and obtain the slope. 12. Set up model of household wiring including ring main circuit. Study the function of switches and fuses. Teachers may feel free to alter or add to the above list. The students may perform about 10 experiments. Some experiments may be demonstrated. EVALUATION The practical work/project work are to be evaluated by the subject teacher and by an External Examiner. (The External Examiner may be a teacher nominated by the Head of the school, who could be from the faculty, but not teaching the subject in the relevant section/class. For example, a teacher of Physics of Class VIII may be deputed to be an External Examiner for Class X, Physics projects.) The Internal Examiner and the External Examiner will assess the practical work/project work independently. Award of marks (20 Marks) Subject Teacher (Internal Examiner) 10 marks External Examiner 10 marks The total marks obtained out of 20 are to be sent to the Council by the Head of the school. The Head of the school will be responsible for the entry of marks on the mark sheets provided by the Council.

CONTENTS 1.

Force

13-29 29

2.

Work, Power and Energy

30-50

3.

Machines

51-67

4.

Refraction of Light at Plane Surfaces

68-94

5.

Refraction of Light Through a Lens

95-120

6.

The Electromagnetic Spectrum

121-133

7.

Sound

134-156

8.

Electric Current

157-178

9.

Electrical Energy and Household Circuits

179-199

10.

Electromagnetism

200-224

11.

Heat

225-244

12.

Modern Physics

245-263

1 FORCE LEARNING OUTCOMES zTorque,

Circular Motion : Centripetal Force and Centrifugal Force.

zUniform

Equilibrium and Centre of Gravity.

The word ‘force’ is used commonly in our everyday life. Generally, we say that we use force to walk, to talk, to lift objects, to push or pull objects or to even EJCPIGVJGUJCRGQHQDLGEVU5QOGEQOOQPGZCORNGU include pulling a rope, pushing a pin on a paper, squeezing a lemon, stretching a rubber band, lifting a bucket of water and so on.

In physics, force is the cause of the change of state of rest or state of motion in a body, or it is used to denote an action that deforms a body. )RUFHLVDQH[WHUQDOLQIOXHQFHWKDWFKDQJHVRUWHQGVWR FKDQJH WKH VWDWH RI UHVW RU PRWLRQ RI D ERG\ RU GHIRUPV D ERG\WKDWLVFKDQJHVLWVVKDSHDQGVL]H Force is a vector quantity. Its S.I. unit is Newton.

(A) TORQUE, EQUILIBRIUM AND CENTRE OF GRAVITY 1.1 TRANSLATIONAL AND ROTATIONAL MOTION

TQCFCDCNNTQNNKPIQPVJGƀQQTKPCUVTCKIJVNKPGRCVJ (Fig. 1.1) and so on.

A rigid body is a body that does not get deformed under the action of a force. Ideally, no real body is truly rigid; however, wood, stone, metals, glass and so on can be regarded as rigid bodies. A rigid body can have two types of motion, translational and rotational.

Fig. 1.1 : Translational motion.

2. Rotational motion : This type of motion occurs 1. Translational motion : It is also called OLQHDU when the force is applied on a body that is pivoted or motion. In translational motion, the body moves along ſZGF KP UQOG YC[ (KI  6JG TQVCVKQP OC[ QEEWT a straight-line path in the direction of force applied. CTQWPFCſZGFCZKUUWEJCUVJGTQVCVKQPQHCEGKNKPIHCP In this type of motion, the rigid body is not pivoted or the rotation may occur along with the oscillation of QTſZGFKPCP[YC[CPFGXGT[RCTVKENGQHVJGDQF[JCU VJGCZKUUWEJCUVJGTQVCVKQPQHCPQUEKNNCVKPIVCDNGHCP the same displacement. Examples : Rotation of a potter’s wheel, a merryExamples : Motion of a rectangular wooden block go-round, a spinning top, movement of a door around down the inclined plane, a car moving on a straight the hinges, a wheel of a vehicle and so on.

14

CERTIFICATE PHYSICS–X

Merry-go-round

Factors Affecting the Moment of a Force

The two factors affecting the moment or turning of a force are as follows : 1. The magnitude of the force (F) applied. r  6JG RGTRGPFKEWNCT FKUVCPEG QH NKPG QH CEVKQP QH F VJGHQTEG :;HTQOVJGRQKPVQHCEVKQPQTCZKUQH the rotation (AOB). Axis of rotation In Fig. 1.3, OP is a perpendicular drawn from the point O on the line of action of force. This represents Fig. 1.2 : Rotational motion. the distance between the line of action of force,LHXY In general, the motion of a rigid body is a combi- CPFVJGCZKUQHTQVCVKQPLH AOB. nation of translational and rotational motion. 7KHPRPHQWRIIRUFHRUWRUTXHDERXWDSRLQWLVPHDVXUHG The turning or rotational effects of a force shall be E\ WKH SURGXFW RI WKH PDJQLWXGH RI WKH IRUFH DQG WKH SHUSHQGLFXODUGLVWDQFHRIWKHOLQHRIDFWLRQRIIRUFHIURPWKH discussed in the following sections. D[LVRIURWDWLRQ 1.2 MOMENT OR TURNING EFFECTS OF Moment of force about the point O = Force A FORCE/TORQUE × Perpendicular distance of force from the point O W = F × OP %QPUKFGTCTKIKFDQF[ſZGFCVCRQKPV1QPYJKEJ 6JG HCTVJGT VJG NKPG QH CEVKQP HTQO VJG CZKU QH a force F acts at a point P (Fig. 1.3). Point P is called rotation, the more is the turning of a body. In other the SRLQWRIDFWLRQRIWKHIRUFH. An imaginary line passing words, when the perpendicular distance of line of through the point of action of force and drawn in the CEVKQPQHHQTEGKUOCZKOWOHTQOVJGCZKUQHTQVCVKQP same direction in which the force acts is called the OLQH then the given amount of force will produce the RIDFWLRQRIIRUFH. XY is the line of action of force. OCZKOWOVQTSWGVQVWTPVJGDQF[ Rotating disc

Units of Moment of Force/Torque Unit of moment of force = Unit of force × Unit of distance As the SI unit of force is newton and that of distance is metre, the SI unit of moment of force is newton × metre (N m). The CGS unit of moment of force is dyne cm. If the gravitational unit of force is considered, then the units of torque are kgf m and gf cm in the SI and CGS unit, respectively. Relation between the units : Fig. 1.3 : Moment of force. 1 N m = 105 dyne × 10 cm = 107 dyne cm When the line of action passes through the point 1 kgf m = 9.8 N m of action, the force is unable to produce linear motion 1 gf cm = 980 dyne cm in the body as the body is pivoted, but it is capable QH VWTPKPI QT TQVCVKPI VJG DQF[ CDQWV C XGTVKECN CZKU Torque is a YHFWRU quantity. Its magnitude is equal passing through the point O, as shown by line AOB. to the product of force and the perpendicular distance, 6JKU XGTVKECN CZKU KU MPQYP CU D[LV RI URWDWLRQ and the and the direction is normal to the plane containing the turning effect is known as PRPHQWRIIRUFHRUWRUTXH. It perpendicular distance and the force. is represented by the symbol W (tau). Torque is created Clockwise and Anticlockwise Moments when the line of action of a force does not pass through The direction of rotation produced on a body the centre of rotation. can be either clockwise or anticlockwise. It depends 7KHPRPHQWRIDIRUFHRUWRUTXHRQDERG\LVWKHWXUQLQJ on the direction of the force applied and the point HIIHFWRIIRUFHDFWLQJRQWKHERG\DERXWWKHSRLQWRUD[LVRI of application of force. In Fig. 1.4, UA represents URWDWLRQ perpendicular distance from the centre to the line of

FORCE

action of the force. If the force is applied at the point P in the upward direction as shown, the body will rotate in the anticlockwise direction and the moment of force is called DQWLFORFNZLVH PRPHQW. It is taken as SRVLWLYH. Conversely, if the force at point P is applied in the downward direction, then the body will rotate in the clockwise direction and the moment of force is calledFORFNZLVHPRPHQW It is considered QHJDWLYH. F F

F

No torque

˙˙˙˙˙˙ torque

Clockwise torque

Fig. 1.4 : Anticlockwise and clockwise moments.

Examples of turning effect of force 1. Opening and shutting a door : A door is attached on one side to the hinges. A vertical line drawn VJTQWIJVJGJKPIGUHQTOUKVUCZKUQHTQVCVKQP To open or close a door, we apply a force on its handle (LH normal to the door). The handle is provided at the other free end of the door, (at point A) so that the distance from the hinges is more, as shown in Fig. 1.5. If we apply a force at a point somewhere in the middle of the door (point B) or near to the hinges, a much greater force is required to open or (point C)

15

close the door, and if we apply a force on the hinges of the door, the door will not open or close even if the magnitude of force is large, because the line of action is passing through the point of rotation. The handles being at a large perpendicular distance from the hinges of the door, comparatively a much smaller force is required to be applied on the handles to open or close the doors. A smaller force on the handle at the free end will produce the same turning effect as a larger force on the handle if it is located nearer to the hinges. It is due to this reason the handle is provided near the free end of the door. 2. Turning of a see-saw : In a see-saw, the fulcrum CVVJGEGPVTGKUVJGCZKUQHTQVCVKQP+HVYQEJKNFTGPQH roughly the same weight sit on the two ends of a seesaw, at points equidistant from the fulcrum, then the UGGUCYKUKPGSWKNKDTKWOCUVJGVYQEJKNFTGPGZGTVCP equal force (due to their weight) in opposite direction. However, if on one side of the see-saw a child is sitting and on the other side an adult person with heavier weight is sitting, as shown in Fig. 1.6 (a), then due to the greater force of the adult person, the see-saw will turn anticlockwise. To maintain an equilibrium or balance Fig. 1.6 (b), the adult person needs to sit closer to the fulcrum, as this decreases the perpendicular FKUVCPEG QH NKPG QH CEVKQP QH HQTEG HTQO VJG CZKU QH rotation (resulting in a lesser turning effect).

Fulcrum

d F (a)

Axis of rotation

Fulcrum

Hinges

C

B

Handle A (b)

Fig. 1.6 : Turning a see-saw. Fig. 1.5 : Opening/shutting a door.

3. Turning of a steering wheel : A driver has to turn the steering wheel to change the direction of a

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