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Mechanics-I: Quick Revision of Formulae for IIT JEE, UPSEE & WBJEE

Dec 15, 2016 15:27 IST

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.

Mechanics-I

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 Set-1

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 = Ap Bq/Cr, 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] = [M0 L3 T0]

             [v] = [M0LT−1]

             [F] = [MLT−2]

             [ρ] = [ML−3T0]

JEE Main Mathematics Solved Sample Paper Set-VII

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 Set-VII

KINEMATIC EQUATIONS FOR UNIFORMLY ACCELERATED MOTION

    

    where, Δx = displacement (final position – initial  position),

    v = velocity or speed at any time, vo = 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.

            FAB  =  −FBA 

          (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 free-body diagram of that part.
  • In a free-body 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, Kf  −  Ki = 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 xfxi

       

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 horse-power (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 Set-VII

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