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Summary Phy Formula Handbook Class 11

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If you struggle with remembering formulas of physics and want to elevate the game, this Formula Handbook is for you. Now it will be a child's play to learn all the formulas as this study guide will help you!

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ALL YOU NEED STUDY GUIDE AND FORMULA HANDBOOK. PHY CLASS 11

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Physics Sankalp
NEET Formula Handbook

Chapter‐1 Basic Mathematics
Cosine law
formulae used in Physics cos 𝐴 , cos 𝐵
Quadratic Equation 𝐶
√
, cos
Roots of 𝑎𝑥 𝑏𝑥 𝑐 0 𝑎𝑟𝑒 𝑥
Sum of roots 𝑥 𝑥 ; Product of roots 𝑥 𝑥
Binomial Approximation
If x << 1, then 1 𝑋 1 𝑛𝑥 & 1 𝑋 1 𝑛𝑥
Logarithm
Log mn=log m+log n
log m/n = log m – log n
log mn = n log m
log 𝑚 2.303 log 𝑚
log 2 = 0.3010
Componendo And Dividendo Law
𝑝 𝑎 𝑝 𝑞 𝑎 𝑏
𝐼𝑓 𝑡ℎ𝑒𝑛 Approximation for small 𝜽
𝑞 𝑏 𝑝 𝑞 𝑎 𝑏 • sin 𝜃 ≈ 𝜃
Arithmetic Progression‐Ap Formula • cos 𝜃 ≈ 1
A, a+d, a + 2d, a + 3d, …, a + (n ‐ ) d, here d = common • tan 𝜃 ≈ 𝜃 ≈ sin 𝜃
difference Differentiation
Sum of n terms 𝑆 2𝑎 𝑛 1 𝑑
•𝑦 𝑥 → 𝑛𝑥
NOTES
•𝑦 𝐼𝑛𝑥 →
(i) 1 + 2 + 3 + 4 + 5 … +_ n =
• y=sin x→ cos 𝑥
(ii) 1 2 3 … 𝑛
Geometrical Progression‐Gp Formula • y=cos x→ sin 𝑥
A, ar, 𝑎𝑟 , … here, r = common ratio •𝑦 𝑒 → 𝛼𝑒
• y = uv → 𝑢 𝑣 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑟𝑢𝑙𝑒
Sum of n terms 𝑆
• y=f (g(x)) → (Chain rule)
Sum of ∞ terms 𝑆 =
Trigonometry •𝑦 𝑘 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ⇒ 0
• 2𝜋 𝑟𝑎𝑑𝑖𝑎𝑛 360° ⇒ 1 𝑟𝑎𝑑 57.3°
•𝑦 ⇒ 𝐷𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑅𝑢𝑙𝑒
• cosec 𝜃
Integration
• sec 𝜃
• 𝑋 𝑑𝑥 𝐶, 𝑛 1
• cot 𝜃 • 𝑑𝑥 ℓ𝑛𝑥 𝐶
• sin 𝜃 cos 𝜃 1
• 𝑠𝑖𝑛 𝑥𝑑𝑥 cos 𝑥 𝐶
• 1 tan 𝜃 sec 𝜃
•1 cot 𝜃 cosec 𝜃 • 𝑐𝑜𝑠 𝑥𝑑𝑥 sin 𝑥 𝐶
• sin 𝐴 𝐵 cos 𝐴 cos 𝐵 sin 𝐴 sin 𝐵
• 𝑒 𝑑𝑥 𝑒 𝐶
• cos 𝐴 𝐵 cos 𝐴 cos 𝐵 ∓ sin 𝐴 sin 𝐵
𝛼𝑥 𝛽
tan 𝐴 𝐵 • αx β 𝑑𝑥
∓ 𝛼 𝑛 1
• sin 2A = 2 sin A cos A Maxima and Minima of a Function y = f(x)
• cos 2A = cos 𝐴 sin 𝐴 1 2 sin 𝐴
2 cos 𝐴 1 • For maximum value 0& 𝑣𝑒
• tan 2A = • For maximum value 0& 𝑣𝑒
Sine law Average of a Varying Quantity
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, Physics Sankalp
NEET Formula Handbook

If y = f(x) then < y > = 𝑦
Formulae for calculation of Area
• Area of a square = 𝑠𝑖𝑑𝑒
• Area of rectangle = length × breadth
• Area of a triangle = ½ × base × height
• Area of a trapezoid = ½ × (distance between parallel
sides) × (sum of parallel sides)
• Area enclosed by a circle = 𝜋 𝑟 𝑟 𝑟𝑎𝑑𝑖𝑢𝑠
• Surface area of a sphere = 4𝜋 𝑟 𝑟 𝑟𝑎𝑑𝑖𝑢𝑠
• Area of a parallelogram = base × height
• Area of curved surface of cylinder = 2𝜋 𝑟𝑙 (r = radius
and l = length)
• Area of whole surface of cylinder = 2𝜋𝑟 (r + l) (l =
length)
• Area of ellipse = 𝜋 ab (a & b are semi major and semi Chapter 2‐ Units and Measurement
minor axis respectively).
• Surface area of a cube = 6(side)2 System of Units: A complete set of units both
Volume of Geometrical Figures fundamental and derived for all kinds of physical
• Volume of a sphere = 𝜋 𝑟 (r = radius) quantities is called system of units.
• Volume of a cylinder = 𝜋 𝑟 𝑙 (r = radius and l = length) S. MKS CGS FPS
• Volume of a cone = 𝜋 𝑟 ℎ (r = radius and h = height) No.
Some Basic Plots 1. Length (m) Length (cm) Length (ft.)
• Straight Line 2. Mass (kg) Mass (g) Mass(pound)
y = mx + c (where m is the slope of the line and c is the y 3. Time (s) Time (s) Time (s)
intercept)

Unit : The reference standard used for the measurement
of a physical quantity is called a unit.

Fundamental Quantities: The physical quantities which
do not depend on any other physical quantities for their
measurements are known as fundamental quantities.

Derived Quantities: The physical quantities which
depends on one or more fundamental quantities for
• Parabola their measurements are known as derived quantities.
y = 𝑎𝑥
Parallax Method: The method used to measure large
distances are called Parallax Method.

Distance of an object by parallax method, 𝐷

Dimensional Analysis: The dimensions of a physical
quantity are the powers to which fundamental units
must be raised in order to obtain the unit of the given
physical quantity.
• Exponential function
y=𝑒

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, Physics Sankalp
NEET Formula Handbook
Application of Dimensional Analysis Error of Division

• To check the dimensional consistency of a given 𝑍
physical relationship.

• To derive relationship between various physical ∴
quantities.
Error in case of raised power
• To convert units of a physical quantity from one
system to another Z

Error: The difference between the true value and ∴ 𝑝⋅ 𝑞⋅ 𝑟⋅
measured value of physical quantity is called error.

Error Analysis:
𝑎 , 𝑎 , 𝑎 , … … 𝑎 values obtained in measurement. Chapter‐3 Scalars and Vector
⋯…..
𝑎mean
Vector Quantity‐ A physical quantity which requires
|Δ𝑎 | 𝑎 𝑎mean magnitude and a particular direction for its complete
|Δ𝑎 | 𝑎 𝑎mean
expression.
|Δ𝑎 | 𝑎 𝑎mean
| | | | ⋯…..| | ⃗
Δ𝑎mean Unit vectors: 𝐴
Relative error mean Scalar Quantity: A physical quantity which can be
mean
completely described by its magnitude only is known as
Percentage error mean
100 scalar quantity.
mean

Parallel Vector: Those vectors which have the same
Types of Errors‐
directions are called as parallel vectors.
Absolute error: The magnitude of the difference
Equal Vector: Vectors which have equal magnitude and
between the individual measurement and the true value
same direction are called equal vectors.
of the quantity is called absolute error.
Anti‐parallel Vectors: Those vectors which have the
Mean absolute error: The arithmetic mean of all the
opposite directions are called as Antiparallel vectors.
absolute errors is called mean absolute error.
Opposite Vectors: Vectors have equal magnitude but
Relative error: The ratio of mean absolute error in the
opposite directions are called as opposite vectors.
measurement of a physical quantity to its most probable
value is called relative error. Unit Vectors: Vectors whose magnitude is one is called a
unit vector
Percentage error: The relative error multiplied by 100 is
called the percentage error Law of Triangle:
Combination of Errors: 𝑅⃗ 𝐴⃗ 𝐵⃗

Error of sum or difference
Z 𝐴 𝐵
Δ𝑍 Δ𝐴 Δ𝐵

Error of product Law of Polygon:
If some vectors are represented by sides of a polygon in
𝑍 𝐴𝐵 same order, then their resultant vector is represented by
the closing side of polygon in the opposite order.

#SankalpSelectionKa

, Physics Sankalp
NEET Formula Handbook

𝑅⃗ 𝐴⃗ 𝐵⃗ 𝐶⃗ 𝐷⃗ 𝐴
𝑐𝑜𝑠𝛽
𝐴
𝐴
𝑐𝑜𝑠 𝛾
𝐴
cos 𝛼 cos 𝛽 cos 𝛾 1
sin 𝛼 𝑠𝑖𝑛 𝛽 sin 𝛾 2
Dot Product:
Law of Parallelogram:
𝐴⃗ ∙ 𝐵⃗ 𝐴𝐵 𝑐𝑜𝑠 𝜃
If two vectors are represented by two adjacent sides of a
parallelogram which are directed away from their
common point then their sum (i.e. resultant vector) is
given by the diagonal of the parallelogram passing away
through that common point
𝑅⃗ 𝐴⃗ 𝐵⃗
𝑅 𝐴 𝐵 2𝐴𝐵 𝑐𝑜𝑠𝜃 Key points
1) If Q = 0, 𝐴⃗ ∙ 𝐵⃗ 𝐴𝐵
If Q = 90, 𝐴⃗ ∙ 𝐵⃗ 0
If Q = 180, 𝐴⃗ ∙ 𝐵⃗ 𝐴𝐵
2) Angle between two vectors
𝐴⃗ ∙ 𝐵⃗
cos 𝜃
𝐴𝐵
3) It is commutative
Cases
1) If 𝜃 = 0, R = A + B 𝐴⃗ ∙ 𝐵⃗ 𝐵⃗ ∙ 𝐴⃗
4) It is Distributive
2) If 𝜃 = 90, R = √𝐴 𝐵
𝐴⃗ ∙ 𝐵⃗ 𝐶⃗ 𝐴⃗ ∙ 𝐵⃗ 𝐵⃗ ∙ 𝐶⃗
3) If 𝜃 = 180, R = A – B
Subtraction of vectors: 5) It is associative
𝐴⃗ 𝐵⃗ 𝐶⃗ 𝐷⃗ 𝐴⃗ ∙ 𝐶⃗ 𝐴⃗ ∙ 𝐷⃗ 𝐵⃗ ∙ 𝐶⃗ 𝐵⃗ ∙ 𝐷⃗
𝑅 𝐴 𝐵 2𝐴𝐵 cos 𝜃
6) In case of orthogonal vectors
𝑖∙𝑗 𝑗∙𝑘 𝑘∙𝑖 0
7) Scalar product of a vector by itself
𝐴⃗ ∙ 𝐴⃗ 𝐴
8) In case of unit vector
𝑖∙𝑖 𝑗∙𝑗 𝑘∙𝑘 1
9) In terms of components
𝐴⃗ ∙ 𝐵⃗ 𝐴 𝐵 𝐴 𝐵 𝐴 𝐵
Resolution of vectors 10) Projection of vector
⃗∙ ⃗
a) Two dimensions Projection of 𝐵⃗ on to 𝐴⃗ 𝐵 cos 𝜃
⃗∙ ⃗
Projection of 𝐴⃗ on to 𝐵⃗ 𝐴 cos 𝜃
Cross product:
𝐶⃗ 𝐴⃗ 𝐵⃗
𝐶 𝐶⃗ 𝐴𝐵𝑠𝑖𝑛 𝜃

b) Three dimensions
𝐴⃗ 𝐴 𝑖 𝐴 𝑗 𝐴 𝑘
𝐴 𝐴 𝐴 𝐴

cos 𝛼

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