CIRCULAR MOTION(FORMULAS & MCQs) | Additional Study Material for NEET PDF Download

 Page 2


 
No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanical 
including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher. 
 
 
STD. XII Sci. 
Triumph Physics 
 
Based on Maharashtra Board Syllabus 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
Printed at: Dainik Saamana, Navi Mumbai 
Useful for all Agricultural, Medical, Pharmacy and Engineering Entrance Examinations  
held across India.   
TEID : 929 
Solutions/hints to Evaluation Test available in downloadable PDF format at
www.targetpublications.org/tp929 
Salient 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, MH CET 2014, 2015  
•  Evaluation test provided at the end of each chapter 
 
Fourth Edition: June 2015
Page 3


 
No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanical 
including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher. 
 
 
STD. XII Sci. 
Triumph Physics 
 
Based on Maharashtra Board Syllabus 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
Printed at: Dainik Saamana, Navi Mumbai 
Useful for all Agricultural, Medical, Pharmacy and Engineering Entrance Examinations  
held across India.   
TEID : 929 
Solutions/hints to Evaluation Test available in downloadable PDF format at
www.targetpublications.org/tp929 
Salient 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, MH CET 2014, 2015  
•  Evaluation test provided at the end of each chapter 
 
Fourth Edition: June 2015
Preface 
 
“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. 
The content of this book is based on the Maharashtra State Board Syllabus. Formulae that form a vital part of 
MCQ solving are provided in each chapter. Notes provide important information about the topic. Shortcuts provide 
easy and less tedious solving methods. Mindbenders have been introduced to bridge the gap between a text book 
topic and the student’s understanding of the same. A quick reference to the notes, shortcuts and mindbenders has been 
provided 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,  G CET, Assam CEE, BCECE, EAMCET (Engineering, Medical) 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 the 
student on a competitive level.  
An additional feature called “The physics of .....” has been included in the book to foster a keen interest in 
the subject of physics. 
 The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’ve 
nearly missed something or want to applaud us for our triumphs, we’d love to hear from you. 
Please write to us on : mail@targetpublications.org  
   
 
Best of luck to all the aspirants! 
 
Yours faithfully  
Authors 
 
 
 
 
 
 
Sr. 
No. 
Topic Name Page No. 
1 Circular Motion 1 
2 Gravitation 47 
3 Rotational Motion 91 
4 Oscillations 138 
5 Elasticity 191 
6 Surface Tension 223 
7 Wave Motion 254 
8 Stationary Waves 291 
9 
Kinetic Theory of Gases and 
Radiation 
332 
10 Wave Theory of Light 396 
Sr. 
No. 
Topic Name Page No. 
11 Interference and Diffraction 421 
12 Electrostatics 462 
13 Current Electricity 513 
14 
Magnetic Effects of Electric 
Current 
542 
15 Magnetism 577 
16 Electromagnetic Induction 595 
17 Electrons and Photons 646 
18 
Atoms, Molecules and 
Nuclei 
672 
19 Semiconductors 715 
20 Communication Systems 749 
  
Page 4


 
No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanical 
including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher. 
 
 
STD. XII Sci. 
Triumph Physics 
 
Based on Maharashtra Board Syllabus 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
Printed at: Dainik Saamana, Navi Mumbai 
Useful for all Agricultural, Medical, Pharmacy and Engineering Entrance Examinations  
held across India.   
TEID : 929 
Solutions/hints to Evaluation Test available in downloadable PDF format at
www.targetpublications.org/tp929 
Salient 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, MH CET 2014, 2015  
•  Evaluation test provided at the end of each chapter 
 
Fourth Edition: June 2015
Preface 
 
“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. 
The content of this book is based on the Maharashtra State Board Syllabus. Formulae that form a vital part of 
MCQ solving are provided in each chapter. Notes provide important information about the topic. Shortcuts provide 
easy and less tedious solving methods. Mindbenders have been introduced to bridge the gap between a text book 
topic and the student’s understanding of the same. A quick reference to the notes, shortcuts and mindbenders has been 
provided 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,  G CET, Assam CEE, BCECE, EAMCET (Engineering, Medical) 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 the 
student on a competitive level.  
An additional feature called “The physics of .....” has been included in the book to foster a keen interest in 
the subject of physics. 
 The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’ve 
nearly missed something or want to applaud us for our triumphs, we’d love to hear from you. 
Please write to us on : mail@targetpublications.org  
   
 
Best of luck to all the aspirants! 
 
Yours faithfully  
Authors 
 
 
 
 
 
 
Sr. 
No. 
Topic Name Page No. 
1 Circular Motion 1 
2 Gravitation 47 
3 Rotational Motion 91 
4 Oscillations 138 
5 Elasticity 191 
6 Surface Tension 223 
7 Wave Motion 254 
8 Stationary Waves 291 
9 
Kinetic Theory of Gases and 
Radiation 
332 
10 Wave Theory of Light 396 
Sr. 
No. 
Topic Name Page No. 
11 Interference and Diffraction 421 
12 Electrostatics 462 
13 Current Electricity 513 
14 
Magnetic Effects of Electric 
Current 
542 
15 Magnetism 577 
16 Electromagnetic Induction 595 
17 Electrons and Photons 646 
18 
Atoms, Molecules and 
Nuclei 
672 
19 Semiconductors 715 
20 Communication Systems 749 
  
 
 
 
 
 
Publications Pvt. Ltd.  
Target Chapter 01: Circular Motion
 1
 
 
 
 
 
 
 
 
 
 
Syllabus 
 
 
1.0 Introduction 
 
1.1 Angular displacement 
 
1.2 Angular velocity and angular 
acceleration 
 
1.3  Relation between linear velocity and 
angular velocity 
 
1.4  Uniform circular motion 
 
1.5 Acceleration in U.C.M  
(Radial acceleration) 
 
1.6 Centripetal and centrifugal forces 
 
1.7 Banking of roads 
 
1.8 Conical pendulum 
 
1.9 Vertical circular motion 
 
1.10 Kinematical equation for circular motion in analogy with linear motion 
 
 
 
 
 
 
Circular Motion 
01 
Riding on a vertical circular arc, this roller
coaster fans experience a net force and
acceleration that point towards the centre of the
circle 
Page 5


 
No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanical 
including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher. 
 
 
STD. XII Sci. 
Triumph Physics 
 
Based on Maharashtra Board Syllabus 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
 
 
Printed at: Dainik Saamana, Navi Mumbai 
Useful for all Agricultural, Medical, Pharmacy and Engineering Entrance Examinations  
held across India.   
TEID : 929 
Solutions/hints to Evaluation Test available in downloadable PDF format at
www.targetpublications.org/tp929 
Salient 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, MH CET 2014, 2015  
•  Evaluation test provided at the end of each chapter 
 
Fourth Edition: June 2015
Preface 
 
“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. 
The content of this book is based on the Maharashtra State Board Syllabus. Formulae that form a vital part of 
MCQ solving are provided in each chapter. Notes provide important information about the topic. Shortcuts provide 
easy and less tedious solving methods. Mindbenders have been introduced to bridge the gap between a text book 
topic and the student’s understanding of the same. A quick reference to the notes, shortcuts and mindbenders has been 
provided 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,  G CET, Assam CEE, BCECE, EAMCET (Engineering, Medical) 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 the 
student on a competitive level.  
An additional feature called “The physics of .....” has been included in the book to foster a keen interest in 
the subject of physics. 
 The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’ve 
nearly missed something or want to applaud us for our triumphs, we’d love to hear from you. 
Please write to us on : mail@targetpublications.org  
   
 
Best of luck to all the aspirants! 
 
Yours faithfully  
Authors 
 
 
 
 
 
 
Sr. 
No. 
Topic Name Page No. 
1 Circular Motion 1 
2 Gravitation 47 
3 Rotational Motion 91 
4 Oscillations 138 
5 Elasticity 191 
6 Surface Tension 223 
7 Wave Motion 254 
8 Stationary Waves 291 
9 
Kinetic Theory of Gases and 
Radiation 
332 
10 Wave Theory of Light 396 
Sr. 
No. 
Topic Name Page No. 
11 Interference and Diffraction 421 
12 Electrostatics 462 
13 Current Electricity 513 
14 
Magnetic Effects of Electric 
Current 
542 
15 Magnetism 577 
16 Electromagnetic Induction 595 
17 Electrons and Photons 646 
18 
Atoms, Molecules and 
Nuclei 
672 
19 Semiconductors 715 
20 Communication Systems 749 
  
 
 
 
 
 
Publications Pvt. Ltd.  
Target Chapter 01: Circular Motion
 1
 
 
 
 
 
 
 
 
 
 
Syllabus 
 
 
1.0 Introduction 
 
1.1 Angular displacement 
 
1.2 Angular velocity and angular 
acceleration 
 
1.3  Relation between linear velocity and 
angular velocity 
 
1.4  Uniform circular motion 
 
1.5 Acceleration in U.C.M  
(Radial acceleration) 
 
1.6 Centripetal and centrifugal forces 
 
1.7 Banking of roads 
 
1.8 Conical pendulum 
 
1.9 Vertical circular motion 
 
1.10 Kinematical equation for circular motion in analogy with linear motion 
 
 
 
 
 
 
Circular Motion 
01 
Riding on a vertical circular arc, this roller
coaster fans experience a net force and
acceleration that point towards the centre of the
circle 
 
 
 
 
 
Publications Pvt. Ltd.  
Target 
Std. XII : Triumph Physics
2 
 
 
 
 
 
1. Uniform Circular Motion (U.C.M.): 
 i. Instantaneous angular velocity,   
  ? = 
t0
lim
??
= 
t
??
?
 = 
v
r
 = 2 ?n = 
2
T
?
 
 ii. Average angular velocity, 
  ?
av
 = 
21
21
??
tt
-
-
 = 
?
t
D
D
 
  where, 
  ?
1
 = angular position of the body at time 
t
1
 
  ?
2
 = angular position of the body at time 
t
2
 
 iii. ? = ?
av
 for U.C.M. 
 iv. If a particle makes n rotations in t 
second, then 
  ?
av
 = 
2pn
t
 
 v. Angular acceleration = ? = 0 
 vi. Instantaneous angular acceleration, 
  ?
inst
 = 
t0
?
lim
t
D?
D
D
 = 
d?
dt
 = 
2
2
d?
dt
 
 vii. Average angular acceleration, 
  ?
ave.
 = 
21
21
??
tt
-
-
 = 
?
t
D
D
 
  where, ?
1
 = instantaneous angular speed 
at time t
1 
  ?
2
 = instantaneous angular speed at time 
t
2
. 
 viii. Linear acceleration  
  = centripetal acceleration = 
?
?? v
?
 
          = a = v ? = 
2
v
r
 = r ?
2
 = 4 ?
2
f
2
r = 
2
2
4r
T
?
 
 ix. Time period = T = 
1
frequency(f )
 = 
2 ?
?
 
 x. Relation between linear and angular 
velocity: v
?
= 
?
? ? r
?
= r ? as ? = 90 ? 
 
2. Non-uniform circular motion: 
 i. Radial component of acceleration, 
  a
r
 = ? ?
2
r = ?
2
v
r
 
 ii. Tangential component of acceleration, 
  a
t
 = 
dv
dt
 
 iii. Net (linear) acceleration, 
  a = 
22
rt
aa + ….(Magnitude only) 
  = 
2
2
vdv
rdt
æö
æö
÷ ç ÷ ç
÷ + ÷ ç
ç
÷
÷ ç ç
÷ ç èø
èø
 
 iv. Relation between tangential and angular 
acceleration, 
  
T
ar
?? ?
? ?? = r? 
 ? ? = 0 
 
3. Centripetal force: 
 i. Centripetal force, F
cp 
=
2
mv
r
 
  = mr ?
2
 = mv ? = mr (2 ?f)
2
  
  = mr
2
2
T
? ??
??
??
= 
2
2
T
mr 4 ?
 
 ii. Magnitude of Centrifugal force,  
  =  Magnitude of Centripetal force  
  i.e F
cf
 = 
2
mv
r
 (in magnitude) 
 iii. When an electron moves round the 
nucleus of an atom along a circular path, 
we have 
  
2
2
0
Ze
4r ? ?
= 
2
mv
r
 = m ?
2
r  
  = m 4 ?
2 
n
2
r  = m
2
2
4r
T
?
 
  where, Z = atomic number of the 
nucleus. 
 
4. Motion of a vehicle on a curve road: 
 The maximum velocity v, with which a 
vehicle can take a safe turn so that there is no 
skidding, is  v = rg ?
 
 where, ? = coefficient of limiting friction 
between the wheels and the road.   
   
5. Banking of roads: 
 The proper velocity or optimum v on a road 
banked by an angle ? with the horizontal is 
given by,  
 v = 
s
s
tan
rg
1tan
?? ???
??
???
??
 
 where r = radius of curvature of road 
 g = acceleration due to gravity 
 ?
s
 = coefficient of friction between road and 
tyres  
 when ?
s
 = 0, v = rg tan ?  
Formulae