Physics Syllabus class 11

CBSE SYLLABUS (2018-19)

Unit I: Physical World and Measurement

Chapter–1: Physical World Physics-scope and excitement; nature of physical laws; Physics, technology and society. 

Chapter–2: Units and Measurements Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures. Dimensions of physical quantities, dimensional analysis and its applications. 

Unit II: Kinematics 

Chapter–3: Motion in a Straight Line Frame of reference, Motion in a straight line: Position-time graph, speed and velocity. Elementary concepts of differentiation and integration for describing motion, uniform and non-uniform motion, average speed and instantaneous velocity, uniformly accelerated motion, velocity - time and position-time graphs. Relations for uniformly accelerated motion (graphical treatment). 

Chapter–4: Motion in a Plane Scalar and vector quantities; position and displacement vectors, general vectors and their notations; equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors, relative velocity, Unit vector; resolution of a vector in a plane, rectangular components, Scalar and Vector product of vectors. Motion in a plane, cases of uniform velocity and uniform acceleration-projectile motion, uniform circular motion. 

Unit III: Laws of Motion 

Chapter–5: Laws of Motion Intuitive concept of force, Inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion. Law of conservation of linear momentum and its applications. Equilibrium of concurrent forces, Static and kinetic friction, laws of friction, rolling friction, lubrication. Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road). 

Unit IV: Work, Energy, and Power

Chapter–6: Work, Engery and Power Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power. Notion of potential energy, potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); non-conservative forces: motion in a vertical circle; elastic and inelastic collisions in one and two dimensions. 

Unit V: Motion of System of Particles and Rigid Body

Chapter–7: System of Particles and Rotational Motion Centre of mass of a two-particle system, momentum conservation and center of mass motion. Centre of mass of a rigid body; centre of mass of a uniform rod. Moment of a force, torque, angular momentum, law of conservation of angular momentum and its applications. Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions. Moment of inertia, radius of gyration, values of moments of inertia for simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and their applications. 

Unit VI: Gravitation  

Chapter–8: Gravitation Kepler's laws of planetary motion, universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy and gravitational potential, escape velocity, orbital velocity of a satellite, Geo-stationary satellites. 

Unit VII: Properties of Bulk Matter 

Chapter–9: Mechanical Properties of Solids Elastic behaviour, Stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, shear modulus of rigidity, Poisson's ratio; elastic energy. 

Chapter–10: Mechanical Properties of Fluids Pressure due to a fluid column; Pascal's law and its applications (hydraulic lift and hydraulic brakes), effect of gravity on fluid pressure. Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's theorem and its applications. Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise. 

Chapter–11: Thermal Properties of Matter Heat, temperature, thermal expansion; thermal expansion of solids, liquids and gases, anomalous expansion of water; specific heat capacity; Cp, Cv - calorimetry; change of state - latent heat capacity. Heat transfer-conduction, convection and radiation, thermal conductivity, qualitative ideas of Blackbody radiation, Wein's displacement Law, Stefan's law, Greenhouse effect. 

Unit VIII: Thermodynamics

Chapter–12: Thermodynamics Thermal equilibrium and definition of temperature (zeroth law of thermodynamics), heat, work, and internal energy. First law of thermodynamics, isothermal and adiabatic processes. Second law of thermodynamics: reversible and irreversible processes, Heat engine and refrigerator. 

Unit IX: Behaviour of Perfect Gases and Kinetic Theory of Gases  

Chapter–13: Kinetic Theory Equation of state of a perfect gas, work done in compressing a gas. Kinetic theory of gases - assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro's number. 

Unit X: Mechanical Waves and Ray Optics  

Chapter–14: Oscillations and Waves Periodic motion - time period, frequency, displacement as a function of time, periodic functions. Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a loaded springrestoring force and force constant; energy in S.H.M. Kinetic and potential energies; simple pendulum derivation of expression for its time period. Free, forced and damped oscillations (qualitative ideas only), resonance. Wave motion: Transverse and longitudinal waves, speed of wave motion, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect. 

Chapter–15: RAY OPTICS: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker's formula, magnification, power of a lens, combination of thin lenses in contact, refraction and dispersion of light through a prism. Scattering of light - blue colour of sky and reddish apprearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.

**Syllabus taken from cbse website.

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Unit and Dimensions: Problems

1. In SI system, the unit of Temperature is

    (a) Degree Celcius

    (b) Degree Centigrade

    (c) Degree Kelvin

    (d) Degree Fahrenheit 

[d]

2. Which of the following is a unit of distance?

     (a) Metre

     (b) Astronomical unit

     (c) Light year

     (d)  All of the above

[d]

3. What is the dimension of surface tension:

     (a) $[M^2L^2T^{-2} $

     (b) $[M^2LT^{-2}]$

     (c) $ [ML^0T^{-2}]$

     (d) None of these

[c]

4. Which of the following have the same dimensions?

     (a) Stress

     (b) Bulk modulus

     (c) Thrust

     (d) Energy Density

[a and b]

5. If C and R denote the capacitance and resistance, then the dimension of RC is:

     (a) $[M^0L^0T ]$

     (b) $[ML^0T] $

     (c)  $[MLT]$

     (d)  $[M^0L^0T^2]$

[a]

6. Write any two physical quantities which have the dimension of Energy? [Torque, Work]

7. Is it possible to add any two physical quantities? [No]

8. Force on a sphere of radius 'a' moving in the medium with velocity 'v' is given by $F = 6\pi \eta av $. Find the dimension of $ \eta $. [$ML^{-1}T^{-1}$]

9. What is the dimensional formula for Planck's constant? [$ML^2T^{-1}$]

10. In the formula, $X = 3YZ^2$, X and Z have the dimensions of capacitance and magnetic induction respectively. Find the dimension of Y in MKSQ system. [$M^{-3}L^{-2}T^{4}Q^{4}$]

11. The equation of state for a real gas is given by $ (p+\frac{a}{V^2})(v-b) = RT $. Find the dimensions of 'a' and 'b'. [$[ML^5T^{-2}]$, $[L^3]$]

12. Find the dimension of $\frac{1}{2}\epsilon_0 E^2$. [$ML^{-1}T^{-2}$]

13. A quantity X is given by $ \epsilon_0 L\frac{\Delta V}{\Delta t} $ where $\epsilon_0 $ is the permittivity of the free space, L is the length,  $\Delta$V is the potential difference and ${\Delta t}$ is a time interval. The dimensional formula for X is the same as that of  (a) Resistance (b) Charge (c) Voltage (d) Current. [d]

14. Pressure depends on distance as $ p = \frac{\alpha}{\beta}e^{-\frac{\alpha z}{k \theta}} $, where $\alpha$, $\beta$ are constant, z is the distance, k is Boltzman's constant and $\theta$ is temperature. Find the dimension of $\beta$. [$L^{2}$]

15. Which of the following pair (s) has the same dimension?

     (a) Torque and work

     (b) Angular momentum and Work

     (c) Energy and Young's modulus

     (d) Light-year and Wavelength 

     (e) Reynold number and co-efficient of friction

     (f) Curie and Frequency of the light wave

     (g) Latent heat and gravitational potential

     (h) Planck's constant and torque

[a,d,e,f,g]

16. Let $ [\epsilon_0]$ denote the dimensional formula of permittivity of the vacuum, and $[\mu_0]$ that of permeability of the vacuum. Find their dimensional formula in term of mass M, length L, time T, and electric current I. [$\epsilon_0 = [M^{-1}L^{-3}T^4I^2]$, $\mu_0= [MLT^{-2}I^{-2}]$]

17. Planck's constant h, speed of light c, and gravitational constant G are used to form a unit of length L and a unit of mass M. Then find the correct option (s) is (are): 

   (a) $M \propto \sqrt{c}$ 

   (b) $M \propto \sqrt{G}$ 

   (c) $L \propto \sqrt{h}$ 

   (d) $L \propto \sqrt{G}$

[a,c,d]

18. In term of potential difference V, electric current I, permittivity $\epsilon_0$, permeability $\mu_0$ and speed of light c, the dimensionally correct equation(s) is(are):

    (a) $\mu_0 I^2 = \epsilon_0V^2$ 

    (b) $ \mu_0 I = \epsilon_0V$ 

    (c) $ I = \epsilon_0 cV$ 

    (d) $ \mu_0 c I = \epsilon_0 V$ 

[a,c]

19. A length-scale (l) depends on the permittivity ($\epsilon $) of a dielectric material. Boltzmann constant ($k_B$), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and charge (q) carried by each of the particles. Which of the following expression(s) for l is/are dimensionally correct? 

    (a) $l = \sqrt{\frac{nq^2}{\epsilon k_B T}}$ 

    (b) $l = \sqrt{\frac{\epsilon k_B T}{nq^2}} $ 

    (c) $ l = \sqrt{\frac{q^2}{\epsilon n^{2/3}k_B T}}$ 

    (d) $l = \sqrt{\frac{q^2}{\epsilon n^{1/3}k_B T}}$

[b,d]

20. Give the MKS unit of each of the following: 

    (a) Young's Modulus

    (b) Magnetic Induction

    (c) Power of lens

[$N/m^2$, Tesla, Dioptre]

21. A gas bubble, from an explosion underwater, oscillate with a period T proportional to $p^ad^bE^c$, where  'P' is the static pressure, 'd' is the density of the water, and 'E' is the total energy of the explosion. Find the values of a, b, and c. [$a = -\frac{5}{6},b=\frac{1}{2},c=\frac{1}{3}$]

22. Write the dimensions of the following in terms of mass, time, length, and charge

    (a) Magnetic flux 

    (b) Rigidity modulus

[$[ML^2T^{-1}Q^{-1}], [ML^{-1}T^{-2}]$]

23. Match the following with their dimensions where Q is for charge:

Column I	Column II
(A) Angular momentum	(a) $[ML^2T^{-2}]$
(B) Latent Heat	(b) $[ML^2Q^{-2}]$
(C) Torque	(c) $[ML^2T^{-1}]$
(D) Capacitance	(d) $[ML^3T^{-1}Q^{-2}]$
(E) Inductance	(e) $[M^{-1}L^{-2}T^{2}Q^2]$
(F) Resistivity	(f) $[L^2T^{-2}]$

[$(A) \to (c),(B) \to (f) ,(C)\to (a), (D)\to (e), (E)\to (b),(F)\to (d)$]

24. Match column I with column II:

Column I	Column II
(A) Capacitance	(i)                  Ohm-second
(B) Inductance	(ii)                Coulomb2-joule-1
(C) Magnetic Induction	(iii)               Coulomb (volt)-1
	(iv)               Newton (amp-metre)-1
	(v)                Volt-second (ampere)-1

[$(A) \to (ii),(iii), (B)\to (i),(v), (C)\to (iv)$]

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Mathematics for Physics II

Geometry

1. Two triangles are similar when the ratio of sides is same and angles are same. If two triangles have same configuration i.e. same sides and same angles, then triangles are congruent.

2. Vertical opposite angles are equal.

3. Alternate angles are equal.

4. General Equation of the line is $ y = mx + c$ where m is the slope and c is the intercept.

5. Slope of any line passing through points $ (x_1, y_1) $ and $ (x_2, y_2) $ is $ m = \frac{y_2-y_1}{x_2-x_1} $. Slope is inclination of the line with positive x-axis. If $ \theta $ is the angle made by the line with positive x-axis then slope will be $ m = tan\theta $. For horizontal line, slope is 0 and for vertical line, slope is $ \infty $. 

6. Equation of line passing through points $ (x_1, y_1) $ and $ (x_2, y_2) $ is $ (y-y_1) = \frac{y_2-y_1}{x_2-x_1} (x-x_1) $

7. If we are given two lines, then lines $y=m_1x+c_1$ and $y=m_2x+c_2$ are parallel only when these have the same slopes, i.e. $m_1 = m_2 $. 

8. Two lines $y=m_1x+c_1$ and $y=m_2x+c_2$ are perpendicular when the product of the slopes of two lines is -1, i.e. $m_1m_2 = -1$.

9. Equation of the circle is of form, $ ax^2 + ay^2 + 2bx + 2cy + d = 0 $.

10. Equation of the parabola is either of the form $ (y-c)^2=4a(x-b) $, or $ (x-c)^2 = 4a(y-b) $ or $ y = ax^2 - bx $ or $ x = ay^2-by $.

11. Equation of ellipse is $ \frac{x^2}{a^2}+ \frac{y^2}{b^2}  = 1 $.

12. Equation of hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2}  = 1 $. 

Calculus

1. Function is defined as a operation in which element of the set first are related to elements of second set by some relation. 

Domain of the function is the set all elements (values) which function can take. Range is set of values which function can give. 

Let any function $ y = f(x) $. Let us consider that curve $ y=f(x) $ passes through $(x,y) $. If we need to find the tangent at this point, then slope of the curve will be given by $ m = \frac{dy}{dx}=\frac{d f(x)}{dx} = f'(x) $ where $ \frac{dy}{dx}$ is derivative of y with respect to x.

Derivative of some functions are given below:

1. $ y = constant \implies \frac{dy}{dx}=0$

2. $ y = x^n  \implies \frac{dy}{dx} = nx^{n-1} $ 

3. $ y = sinx \implies \frac{dy}{dx}=cosx$

4. $ y = cosx \implies \frac{dy}{dx}= -sinx $

5. $ y = tanx \implies \frac{dy}{dx}= sec^2x $

6. $ y = lnx \implies \frac{dy}{dx}=\frac{1}{x} $

Some integral formulas:

1. $ \int x^n dx = \frac{x^{n+1}}{n+1} + C $ 

2. $ \int sinx dx = -cosx + C$

3. $ \int cosx dx = sinx + C $

4. $ \int tanx dx = log|sec x| + C$

Problem for Practice:

1. Find the equation of the line which is parallel to the given line $ y = 6x + 4 $ and passes through point (4, 6).

2. Find the  equation of the curve for which every point of the curve is at same distance from the point (3,2).

3. Differentiate the following with respect to x:

 (a) $ y = x^2 + 4x $ 

 (b) $z = 5x^3+10$

 (c) $y = sin4x + log|x|$

 (d) $y = sin^2x$

 (e)$ y = cos5x + tan2x + log|sin x| $

4. Integrate the following functions:

 (a) $y = sinx$

 (b)$y=5x^2 + 4x$

 (c) $y = sin^2x$

 (d) $ y = cos5x $

 (e)$y = logx $

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Mathematics for Physics I

 1. Algebra

Common Formulas:

1. $ (a+b)^2 = a^2+2ab+b^2 $

2. $ (a+b)^3 = a^3+b^3+3a^2b+3ab^2 $

3. $ (a^2-b^2)=(a+b)(a-b) $

4. $ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca $

5. $ (a+b)^2 + (a-b)^2 = 2(a^2+b^2) $

6. $ (a+b)^2 - (a-b)^2 = 4ab $

7. $ (a-b)^3 = a^3-b^3-3a^2b+3ab^2 $

Solving Quadratic Equation: Let any quadratic equation be $ ax^2+bx+c = 0 $. Roots of the equation are given by,  $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} $

If $ {b^2-4ac} = 0 $ then roots are real and equal.

If $ {b^2-4ac} > 0 $ then roots are distinct and real.

If $ {b^2-4ac} < 0 $ then roots are imaginary.

If $ \alpha $ and $ \beta $ are two roots of the equations, then  

Sum of roots: $ \alpha + \beta = \frac{-b}{a} $

Product of roots: $ \alpha \times \beta = \frac{c}{a} $

Difference of roots: $ \alpha - \beta = \frac{\sqrt{b^2 - 4ac}}{a} $

For example, Let $ x^2+x+1=0 $ is a quadratic equation and we need to find the roots of the equation.

For the given equation, $ b^2-4ac = 1 - (4 \times 1 \times 1) = 1-4 = -3  < 0 $

This means that the roots of the equation are imaginary. 

Roots will be, $ x = \frac{-1 \pm \sqrt{-3}}{2} = \frac{-1 - \sqrt{-3}}{2}, \frac{-1 + \sqrt{-3}}{2} $

For $ \sqrt{-1} = i $, then roots will be, \[x = \frac{-1 \pm \sqrt{-3}}{2} = \frac{-1 - \sqrt{3}i}{2}, \frac{-1 + \sqrt{3}i}{2}\]

Binomial Expansion:

If we need to expend $ (1+x)^n $ in powers of x where n is positive integer, we expand it binomially.

Expansion will be 

\[(1+x)^n = 1 + _{1}^{n}{x} + _{2}^{n}{x^2} + ....... + _{i}^{n}{x^i} + ..... + x^n \]

It can be written as \[(1+x)^n = \Sigma _{j=0}^{n} (_{j}^{n} C)(x^j)\]

where \[_{j}^{n} C = \frac{n!}{(n-j)! j!}, n! = n(n-1)(n-2).......3.2.1\] and $ 0! = 1 $.

The number of terms in the expansion of $ (1+x)^n $ are (n+1)

Binomial expansion for any index, i.e. if n is not a positive integer.

\[(1+x)^n = 1 + \frac{n}{1!}x + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + .......... \infty terms\]

If |x| << 1 then $ (1+x)^n = 1 + nx $ i.e. we can ignore highest power of the expansion.

For example: Expand $ (1 + x ) ^ {-2} $.

$ (1+x)^{-2} = 1 + \frac{-2}{1!}x + \frac{-2(-2-1)}{2!}x^2 + \frac{-2(-2-1)(-2-2)}{3!}x^3 + .......... \infty = 1 -2x -3x^2 - 4x^3 + ......  $. 

Try Yourself:

Q1. Find the roots of the equations:

(a) $ x^2 + 2x + 3 = 0 $

(b) $ x^2 - 2x - 3 = 0 $

(c) $ x^2 + 30x  + 1 = 0 $

(d) $ 2x^2 + x + 1 = 0 $

 

Q2. Expand following:

(a) $ (1+x)^7 $

(b) $ (1+x)^{-7} $

(c) $ (1+y)^{-1} $

(d) $ (1+z)^{-10} $

***Solutions of the above problems will be uploaded soon..... 

2. Trigonometry

Relation between arc length, l, radius of the circle, r, and angle $ \theta $ subtended by the arc at the center, \[l = r \theta\]

 

Usefull Trigonometric Formulas for Right Angle Triangle 

Let any right angle triangle with Right angle at B, as shown in the figure click here to see large image. 

1. $ sin A = \frac{a}{b} $

2. $ cosA = \frac{c}{b} $

3. $ tanA = \frac{sin A}{cosA}=\frac{a}{c} $

4. $ cosecA = \frac{1}{sinA}=\frac{b}{a} $

5. $ secA = \frac{1}{cosA}= \frac{b}{c} $

6. $ cot A = \frac{1}{tanA}= \frac{cosA}{sinA}= \frac{c}{a}  $

7. $ sin^2 A + cos^2 A = 1 $ 

8. $ 1 + tan^2 A = sec^2 A $

9. $ 1+ cot^2 A = cosec^2 A $

Above formulas are valid only for Right angle triangle.

In general, for any triangle ABC where A, B and C are the angles, and a, b, and c are the sides opposite to angle A, B and C respectively. 

1. $ \frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c} $

2. $ cos A = \frac{b^2+c^2-a^2}{2bc} $ 

Value of some trigonometric functions:

	0	30	45	60	90
sin	0	$ \frac{1}{2} $	$ \frac{1}{\sqrt{2}}$	$ \frac{\sqrt{3}}{2}$	1
cos	1	$ \frac{\sqrt{3}}{2}$	$ \frac{1}{\sqrt{2}}$	$ \frac{1}{2} $	0
tan	0	$\frac{1}{\sqrt{3}}$	1	$ \sqrt{3} $	$ \infty $

Compound Formula:

1. $ sin(A\pm B) = sinAcosB \pm sinBcosA $

2. $ cos(A\pm B) = cosAcosB \mp sinAsinB $

3. $ tan(A\pm B) = \frac{tanA\pm tanB}{1 \mp tanAtanB} $

4. $sin2A = 2sinAcosA $

5. $ cos2A = cos^2A - sin^2 A = 1 - 2sin^2 A = 2cos^2 A - 1 $

6. $tan2A = \frac{2tanA}{1-tan^2A} $

In the first quadrant, all trigonometric functions have positive values. In second quadrant, sine and cosec are positive and all others are negative. In third quadrant, tan and cot are positive and all others are negative. In fourth quadrant, cos and sec are positive and all other are negative.

1. $ sin(-\theta) = - sin \theta $

2. $ cos(-\theta) = cos \theta $

3. $ tan(-\theta) = - tan \theta $

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