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Physics NumericalsSTD.XII

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.

Edition: June 2014

Prof. Umakant N. Kondapure (M.Sc., B.Ed., Solapur)

Mr. Collin Fernandes (M.Sc., Mumbai)

Mr. Vivek Ghonasgi (M.Sc., B.Ed. Mumbai)

Mrs. Meenal Iyer (M.Sc., Mumbai)

Published by

Target PUBLICATIONS PVT. LTD. Shiv Mandir Sabhagriha, Mhatre Nagar, Near LIC Colony, Mithagar Road, Mulund (E), Mumbai - 400 081 Off.Tel: 022 6551 6551 Email: mail@targetpublications.org Website: www.targetpublications.org

Price : ` 260/-

Printed at: Kings Security Printers Pvt. Ltd. Umbetgam, Valsad - 396170 Target All rights reserved

Publications Pvt. Ltd.

Physics Numericals

STD.XII

Written according to the revised syllabus (2012-2013) published by the Maharashtra State Board of Secondary and Higher Secondary Education, Pune.

TEID : 737

Salient Features :

Subtopic wise numericals with solutions.

Shortcuts to enable quick problem solving.

Practice problems for every subtopic.

Includes solved board numerical.

Numerical based multiple choice questions for effective preparation.

Solutions/hints to practice problems and multiple choice questions available

in downloadable PDF format at www. targetpublications.org

Preface

In the case of good books, the point is not how many you can get through, but rather how many can get through to you. STD XII Sci.: PHYSICS NUMERICALS is a complete and thorough guide to the numerical aspect of the HSC preparation. The book is prepared as per the Maharashtra State Board syllabus .Subtopic wise segregation of Solved Numericals in each chapter help the student to gain knowledge of the broad spectrum of problems in each subtopic Formulae which form a vital part of problem-solving are provided in every chapter. Solutions and calculations have been broken down to the simplest form possible (with log calculation provided wherever needed) so that the student can tackle each and every problem with ease. Problems for practice are provided to test the vigilance and alertness of the students and build their confidence. Board Numericals till the latest year have been provided to help the student get accustomed to the different standards of board numericals. Numerical based multiple choice questions are covered sub-topic-wise to prepare the student on a competitive level. Solution/hints to practice problems and multiple choice questions can be downloaded in PDF format from our website www. targetpublications.org The journey to create a complete book is strewn with triumphs, failures and near misses. If you think weve nearly missed something or want to applaud us for our triumphs, wed love to hear from you. Please write to us on : mail@targetpublications.org

A book affects eternity; one can never tell where its influence stops.

Best of luck to all the aspirants! Yours faithfully Authors R

Contents

Sr. No.

Unit Page No.

1 Circular Motion 1

2 Gravitation 38

3 Rotational Motion 67

4 Oscillations 100

5 Elasticity 129

6 Surface Tension 149

7 Wave Motion 165

8 Stationary Waves 185

9 Kinetic Theory of Gases and

Radiation 212

10 Wave Theory of light 253

Sr. No. Unit Page No.

11 Interference and Diffraction 270

12 Electrostatics 297

13 Current Electricity 329

14 Magnetic Effect of Electric

Current 350

15 Magnetism 373

16 Electromagnetic Induction 389

17 Electrons and Photons 418

18 Atoms, Molecules and Nuclei 433

19 Semiconductors 458

20 Communication System 467

1

Target Publications Pvt. Ltd. Chapter 01: Circular Motion

Formulae Section 1: Angular Displacement, Relation

Between Linear Velocity and Angular Velocity

1. Angular velocity:

i. = rv

where, v = linear velocity r = radius of the circle along which

particle performs circular motion.

ii. = t

where, = angular displacement of the particle in circular motion during time interval t.

iii. = 2n where, n = frequency of revolution of particle

in circular motion.

iv. = T2

where, T = period of revolution of particle performing circular motion.

2. Angular displacement: = t 3. Time period:

i. T = 2 rv ii. T = 2

4. Frequency of revolution:

n = 1T 2

=

5. Linear velocity: i. v = r ii. v = 2nr Section 2: Angular Acceleration 1. Angular acceleration:

i. = t

where, = change in the angular velocity of a particle in circular motion during a time interval t.

ii. = 2 nt

where, n = change in frequency of the particle in circular motion during a time interval t.

Section 3: Centripetal and Tangential Acceleration 1. Centripetal (or radial) acceleration:

ar = rv2 = v = r2

2. Tangential acceleration: aT = r 3. Resultant or total acceleration: a = 2 2t r t ra a 2a a cos+ + where, = angle made by ar with at

a = 2 2t ra a+ when = 90. 4. For U.C.M.:

a = ar = 2vr

= v

at = 0 Section 4: Centripetal and Centrifugal Forces 1. Centripetal force:

i. Fc = rmv2 ii. Fc = mv

iii. Fc = mr2 iv. Fc = 42mrn2

v. Fc = 2

24 mr

T

where, m = mass of particle performing circular motion

Section 5: Motion of a Vehicle along a Curved Unbanked Road

1. The necessary centripetal force:

Fc = mg = 2mv

r

where, m = mass of vehicle v = velocity of the vehicle r = radius of the curve road = coefficient of friction between the tyres

of the vehicle and the surface of the road.

01 Circular Motion

Target Publications Pvt. Ltd. Std. XII Sci.: Physics Numericals

2

2. The maximum velocity with which a vehicle can take a turn safely without skidding:

v = rg 3. The maximum angular velocity with which

a vehicle can take a turn safely without skidding:

= gr

Section 6: Banking of Roads For motion of vehicles along a banked curve road: 1. The proper velocity or optimum velocity: v = rg tan where, = angle of banking 2. The maximum velocity without skidding:

vmax = ss

tanrg1 tan +

where, s = coefficient of friction between the tyres

of the vehicle and surface of the road 3. Angle of banking:

= tan12v

rg

or tan =2v

rg

4. Height of inclined road: h = d sin where, d = distance between the two front or rear

wheels. 5. The maximum velocity with which a vehicle

can go on a banked curved road without toppling:

v = drg2H

where, H = height of centre of gravity (C.G.) of the vehicle from the road.

Section 7: Conical Pendulum 1. Linear speed of bob: v = rg tan 2. Angular velocity:

= gcosl

= g tanr

3. Periodic time:

T = 2 = 2 cos

gl

= 2 hg

where, l = length of conical pendulum h = the height of the fixed support from the

centre of the circle or axial height of the cone

= semivertical angle of the cone. 4. Tension in the string:

T = mgcos

Section 8: Vertical Circular Motion 1. Velocity at any point in vertical circular

motion: i. vP = 2Lv 2gr (1 cos) ii. vL = 5rg

iii. vH = rg

iv. vM = 3rg where, vP = velocity of the particle at any

point P along the circle. vL = Minimum velocity at the lowest

point on the circle so that it can safely travel along the vertical circle (looping the loop).

vH = Minimum velocity of the particle at the highest point on the circle so that the string will not be slackened.

vM = Minimum velocity of the particle at a mid-way point so that it can travel along the circle.

r = radius of the vertical circle. = angle between the position vectors

at the given position of particle and that of the lowest point on the vertical circle.

2. Relation between velocities at different points in vertical circular motion:

i. 2Lv = 2Hv + 4gr

ii. 2Mv = 2Hv + 2gr

3

Target Publications Pvt. Ltd. Chapter 01: Circular Motion3. Tension at: i. Any point P,

TP = 2mv

r+ mg cos

ii. Lowest point L,

TL = 2Lmv

r + mg =

2Hmv

r + 5mg

iii. Highest point H,

TH = 2Hmv

r mg =

2Lmv

r 5 mg

iv. Midway point M,

TM = 2Mmv

r=

2Lmv

r 2 mg

4. Total energy at any point:

E = 12

mv2 + mgr (1 cos )

= 52

mgr

Section 9: Kinematical Equations Analogy between translatory motion and circular motion

No. Translatory Motion Circular Motion

1. Linear velocity v = d r

dt

Angular velocity = d

dt

2. Linear acceleration

a = 2

d v d rdt dt

2

= Angular acceleration

= 2

d ddt dt

2

=

3. Linear momentum p

= m v

Angular momentum L = I

4. Linear impulse = F

(t) = p Angular impulse =

(t) = L

5. Force F = m

a Torque

= I

6. Work W = F

. r Work W =

.

7. Kinetic energy of translation

Et