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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)
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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
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 : firstname.lastname@example.org
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Best of luck to all the aspirants! Yours faithfully Authors R
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
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
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
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
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
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
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. 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:
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:
or tan =2v
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:
= g tanr
3. Periodic time:
T = 2 = 2 cos
= 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
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 =
r + 5mg
iii. Highest point H,
TH = 2Hmv
r mg =
r 5 mg
iv. Midway point M,
TM = 2Mmv
r 2 mg
4. Total energy at any point:
E = 12
mv2 + mgr (1 cos )
Section 9: Kinematical Equations Analogy between translatory motion and circular motion
No. Translatory Motion Circular Motion
1. Linear velocity v = d r
Angular velocity = d
2. Linear acceleration
a = 2
d v d rdt dt
= Angular acceleration
d ddt dt
3. Linear momentum p
= m v
Angular momentum L = I
4. Linear impulse = F
(t) = p Angular impulse =
(t) = L
5. Force F = m
6. Work W = F
. r Work W =
7. Kinetic energy of translation