MechanicsI: Quick Revision of Formulae for IIT JEE, UPSEE & WBJEE
Get important formulae from unit MechanicsI for quick revision. These formulae are very useful during competitive examination. This unit includes chapters – Dimension and Measurement, Kinematics, Laws of Motion and Work, Power and Energy
When exams are round the corner then it is not possible to revise complete books so we have come up with unit wise formulas and important terms. Once you have gone through chapters thoroughly and understood it well there is no need to study it again and again. You can only revise important formulas and terms which will save your precious time.
In this regard find Electrostatics and Electric Current important Formulas for Quick Revision. These formulae will be helpful in various engineering entrance examinations such as IIT JEE, UPSEE, WBJEE etc.
In UPSEE and WBJEE where most of questions are asked directly on formulae, this quick revision note is very important.
MechanicsI
SI Base Quantities and Units
Base quantity 
SI Units 

Name 
Symbol 

Length 
metre 
m 
Mass 
kilogram 
kg 
Time 
second 
s 
Electric current 
Ampere 
A 
Thermodynamic Temperature 
Kelvin 
K 
Amount of substance 
Mole 
mole 
Luminous Intensity 
Candela 
cd 
Accuracy, Precision of Instruments and Errors in Measurement
 The result of every measurement by any measuring instrument contains some uncertainty. This uncertainty is called error.
 The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity.
 Precision tells us to what resolution or limit the quantity is measured.
 The smallest value that can be measured by the measuring instrument is called its least count.
UPSEE 2017 Solved Sample Paper Set1
Combination of Errors
 If Z = A + B, then ± ΔZ = ± ΔA ± ΔB where, A and B are two physical quantities, ΔA and ΔB are their absolute errors and ΔZ is error in their sum or difference
 If Z = AB, then ΔZ/ Z = (ΔA/A) + (ΔB/B)
 if Z = A^{p} B^{q}/C^{r}, then ΔZ/Z = p (ΔA/A) + q (ΔB/B) + r (ΔC/C)
Dimensional Formulae and Dimensional Equations
 The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula of the given physical quantity.
 An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity.
 The dimensional equations of volume [V ], speed [v], force [F ] and mass density [ρ] may be expressed as
[V] = [M^{0} L^{3} T^{0}]
[v] = [M^{0}LT^{−1}]
[F] = [MLT^{−2}]
[ρ] = [ML^{−3}T^{0}]
JEE Main Mathematics Solved Sample Paper SetVII
Dimensional Analysis and its Applications
 Checking the Dimensional Consistency of Equations
 Deducing Relation among the Physical Quantities
 Distance is a scalar quantity which refers to "how much an object has travelled" during its motion.
 Displacement is a vector quantity which refers to "the shortest path an object has travelled" during its motion.
 Average velocity is defined as the change in position or displacement (Δx) divided by the time intervals (Δt ), in which the displacement occurs
 Average speed is defined as the total path length travelled divided by the total time interval during which the motion has taken place
 The average acceleration a over a time interval is defined as the change of velocity divided by the time interval
JEE Main Physics Solved Sample Paper SetVII
KINEMATIC EQUATIONS FOR UNIFORMLY ACCELERATED MOTION
where, Δx = displacement (final position – initial position),
v = velocity or speed at any time, v_{o} = initial velocity or speed, t = time, a = acceleration
Graphs:
 When the motion is uniform then, the velocity of object is constant or its acceleration is 0.
 When the body has uniform acceleration or retarded motion, then acceleration is constant.
 Graphs for the uniform accelerated or retarded object is shown below:
The Law of Inertia
 Everybody continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.
Newton’s First Law of Motion
 If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body.
Newton’s Second Law of Motion
 The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
where, p = momentum, a = acceleration
Newton’s Third Law of Motion
 To every action, there is always an equal and opposite reaction.
F_{AB} = −F_{BA}
(force on A by B) = −(force on B by A)
Conservation of Momentum
 The total momentum of an isolated system of interacting particles is conserved.
Friction
 Friction is tangential component of net contact force between two solid bodies in contact.
 A friction between two or more solid objects that are not moving relative to each other is called static friction.
 Like other forces this force also makes a pair of equal and opposite forces acting on two different bodies.
 Direction of frictional force on a body is opposite to the relative motion (or its tendency) of this body with respect to the other body.
Circular Motion
How to Solve Problems in Mechanics
 Draw a diagram showing schematically the various parts of the assembly of bodies, the links, supports, etc.
 Choose a convenient part of the assembly as one system.
 Draw freebody diagram of that part.
 In a freebody diagram, include information about forces (their magnitudes and directions) that are either given or you are sure of (e.g., the direction of tension in a string along its length). The rest should be treated as unknowns to be determined using laws of motion.
 Employ Newton’s third law wherever necessary.
Work
 The change in kinetic energy of a particle is equal to the work done on it by the net force.
Mathematically, K_{f} − K_{i} = W
 The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement.
Mathematically,
W = (F cos θ )d = F.d
Work Done by a Variable Force
 Let f(x) be the variable force, then the area between F(x) vs x graph represent the work done over the displacement x_{f} − x_{i}
Conservation of Mechanical Energy
 According to conservation of total mechanical energy, the total mechanical energy of a system is conserved if the forces, doing work on it, are conservative.
Points to be Noted
Potential Energy of a String
 F = −kx
where, F = spring force, x = displacement from the equilibrium position, k = spring constant
Power
Units of Power
 The SI unit of Power is Watt.
 There is another unit of power, namely the horsepower (hp) 1 hp = 746 W
Collisions
 In all collisions the total linear momentum is conserved i.e. the initial momentum of the system is equal to the final momentum of the system.
 The kinetic energy conservation (even if the collision is elastic) applies after the collision is over and does not hold at every instant of the collision.
JEE Main Chemistry Solved Sample Paper SetVII
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