Physics Classes

Category: 11th Notes

  • Dimensions and uses of dimensions

    Dimensions and uses of dimensions

    Dimensions and uses of dimensions

    Before to read this topic dimensions, students must know fundamental units . To know or read the topic units click here ( Units and measurement);-

    In this topic we will discuss about what is Dimensions and uses of dimensions ?Also what are the limitations of dimensions ? This topic is easy to understand and video related to the  topic is also linked  with the given notes of Dimensions and uses of dimensions .

    UNITS AND DIMENSIONS ASSIGNMENT

    Dimensions and uses of dimensions-

    DIMENSIONS

    When a physical quantity expressed In terms of fundamental units , it is written as a product of different powers of the fundamental quantity is known as the dimension of the physical quantity .

    Some fundamental units are – Length – [L] , Mass – [M] , Time – [T] , Ampere-[A] etc.

    Here –  [L] , [M] , [T] , [A] are called dimensions .

    Dimension of some physical quantity may be written as –

    (i) speed – distance/time =[L]/[T] = [LT-1] , Or , [M0L1T-1] ;

    (II) Acceleration- Change in velocity/time = dimension of velocity/dimension of time   = [LT-1]/[T] =[LT-2]

    (III) Force – Mass x acceleration  = [M] [LT-2]= [MLT-2]    Similarly we can find the dimension of all other physical quantity .

    Uses of dimensions –

    (i) To check the correctness of the formula – [ Principle of Homogeneity – according to this principle for a given formula , the dimension of every term of L.H.S. = dimensions of every term of R.H.S. ]

    {** we must keep in mind that when two physical quantity is added or subtracted there dimensions will be same }

    Lets check the correctness of given formula S= ut + ½  (at2 )

    Here L.H.S.  dimension of  s= [L]

    Dimension of  ut = [LT-1] X [T] = [L]

    Dimension of next term of R.H.S  ½ at2  = [LT-2][T]2 = [L]

    So dimension of R.H.S = [L] + [L] = [L]

    So we can say dimension of LHS = Dimension of RHS , it follows the principle of homogeneity and hence the given formula is correct .

    [ note- using this process we can find the dimensions of unknown physical quantity ]

    (ii) Conversion of unit of a physical quantity – Dimension also help us to convert the unit of a physical quantity from one form to another Ex- MKS to CGS  or vice-versa .

    As we know , when we change the unit then the magnitude of the physical quantity changes but it express the same physical quantity . example – 1 km = 1000m ; here when we changes the unit km to m its numeric value changes but it express the same physical quantity which is distance/displacement .

    So we can say for a given physical quantity    n1u1=n2u2 ;

    Using this we can write-

    n1[M1 a L1 b T1 c ] = n2[M2 a L2 b T2 c ]

    So ,

    n2 = n1 [M1 a L1 b T1 c ]/ [M2 a L2 b T2 c ]

    = [M1/M2]a [L1/L2]b [T1/T2]C ………..Eq(I)

     

    Suppose we have to convert 10 Newton( MKS) force into Dyne (CGS) . At first we have to write the dimension of the physical quantity which is force ( since Newton is the unit of force ) .

    Dimension of force is [MLT-2] i.e. a=1 , b=1,  c=-2  and n1 = 10 ;

    So applying the eq. (i)  n2 = n1  [M1/M2]a [L1/L2]b [T1/T2]C

    n2 = 10 x [ 1kg/1gm] [1m/1cm] [1s/1s]

    n2= 10 x [1000gm/1gm] [ 100cm/1cm ] [1s/1s] = 10 x 105

    10 Newton = 10 x 105 Dyne ;

    Similarly we can convert a physical quantity from one unit to another .

     

    (iii) Deducing relation among the physical quantity –  Dimension is also used to find the actual relationship among the given physical quantities or in another words we can say it is used to derive the formula with the help of given physical quantities .

    Suppose if it is given the pressure (p)  acting on a body depends on force applied (F) and area of cross-section A  ,

    We can write P α Fa Ab

    Or,   P = K  Fa Ab ( Where K is  a constant ) ………………………..(I)

    Dimension of, pressure P = [ ML-1 T-2]

    Dimension of , force F = [MLT-2]

    Dimension of area A = [L2]

    Putting all these values in equation (i) we can write

    [ ML-1T-2] = [MLT-2]a [L2]b

    [ ML-1T-2] = [Ma La+2b T-2a]  , on comparing the power of both sides we get ;

    a=1 , a+2b=-1 and -2a =- 2

    so a=1 and b=-1 . putting these values in eq. 1 we get

    pressure  p = F/A ;

    again , suppose time period (t) of a pendulum depends on mass of the bob ’m’ length of the pendulum ‘l’ and acceleration of the gravity ‘g’. we have to find the formula of the time period .

    we can write

    t α ma lb gc

    or, t = K ma lb gc  ……………..(i)  where K is a constant .

    [M0L0T1] = [ M]a [L]b [LT-2]c = [Ma Lb+c T-2c]

    On comparing we get , a=0 ,b+c=0 and -2c=1

    On solving all the above relations we get , a=0 . b=1/2 and c=-1/2 ; putting all these value in the above eq (i) we get,

    t= Kl1/2g-1/2 here K= 2∏ √l/g .

     

    limitations of dimensions –

    (i) The dimensional method works only when the dependence is of the product time . it does not show the relation in addition or subtraction .

    (ii) The numerical constant having no dimensions cannot be deduced by the method of dimension.

    (iii) the method works only when a physical quantity depends on only three physical quantity . This method is not valid for four or more physical quantity dependence.

    Assignment related to the unit and dimension is also available for the students , which will help the student to solve questions related to these topics  .

    For assignment-1 click here-

      For assignment -2 click here-

     For objective type questions for unit and dimension-

     

     

     

     

     

     

     

     

  • Projectile motion

    Projectile motion

    Projectile motion

    Projectile given horizontal projection and projectile given angular projection

    In this topic we will discuss about projectile given horizontal and projectile given angular projection. And we will derive the expressions for equation of trajectory, time of flight , vertical height , horizontal range and velocity of projectile at any time .

    Projectile motion-

    When a body has given some initial velocity , and body allowed to move in two dimensional motion under the action of gravitational force only ( i.e. there is no any external force acting on the body ) such kind of motion of the body is called projectile motion .

    • Important things to know about the projectile motion- projectile moves with constant horizontal velocity, there are no any external force it means there is no acceleration or retardation in horizontal motion.
    • The vertical velocity changes with time i.e. increases or decreases when moves downward or upward direction respectively under the gravitational acceleration.
    • There is no air resistance ( practically it is not possible in earth surrounding , but considered)
    • The magnitude of acceleration due to gravity remain constant at every point it doesn’t changes even at height or depth.
    • Projectile given horizontal projection-

    • HORIZONTAL PROJECTION
      HORIZONTAL PROJECTION

    Suppose OX a horizontal line is parallel to the ground and oy is vertical height. A body is projected with velocity  u in horizontal direction ,

    so, ux = u and uy = o

    Let t is the time taken by the body to reach from initial point O to final point C ( as shown in fig. ) then ,    horizontal distance X = ux x t  = u x t

    so  t= x /u

    Again for vertical motion  Y = uyt + ½ gt2 = 0 + ½ gt2

    y = ½ g (X/u)2

    or , Y = ½ g X2/u2……………………..(i) This the equation of trajectory which is equation of parabola , then we can say path followed the projectile is parabolic .

     

    Time of flight (T)  – It is the time taken by the projectile to reach from initial to final position , let T is the time of flight and H is the height ,

    Then,  from equation of motion  Y = uy + ½ gT2

    ( but uy =0)

    so, Y= ½ g T2

    or ,  T = √2H/g ………………(ii)

    Horizontal range (R)   – It is the horizontal distance covered by the projectile during its flight . Since there is no acceleration in horizontal direction.

    So , distance = speed x time

    X = R = u x T = u √2H/g .

    Velocity of the projectile at any time ‘t’ –  As shown in fig. at point p  , there are are two components of the velocity ,  vx and vy along horizontal and vertical direction respectively , then , v =  √(vx)2 + (vy)2

    Or , v = √ u2 +(gt)2 ( since , vx = u and vy = gt )

    Let v makes an angle β with the horizontal then , tanβ = vy/vx

    Or , tanβ = gt/u .

    Or , β = tan-1(gt/u) with the horizontal.

    TO SEE THE VIDEO ON PROJECTILE GIVEN HORIZONTAL PROJECTION CLICK HERE-

    Projectile given angular projection- 

    ANGULAR PROJECTION
    ANGULAR PROJECTION

    Suppose a projectile is projected at an angle θ with horizontal , and velocity given to the projectile is ‘u’ . OX and OY are the horizontal and vertical axis respectively . Then the component of velocity along OX and OY are respectively u cosθ  and  u sinθ .

     

    Equation of trajectory-  let  ‘t’ is the time taken by the projectile to reach from point O to point B as shown in fig.

    Then horizontal distance X = u cosθ x t ,

    Or, t=x/ucosθ

    But for vertical motion ,  y= uyt + ½ g t2

    Putting the  value of time in the above equation we get ,

    Y = usinθ .( x/ucosθ)   + ½ g ( x2/ u2 cos2θ) .

    Or , y=  x tanθ + ½ g (x2/u2 cos2θ) …………………….this is the equation of trajectory , which is parabolic . Hence we can say path followed by the projectile is parabolic .

     

    Time of flight (T) –     It is the total time taken by the projectile to reach from initial position to the final position .   Total time of flight ( T) =  ta ( time of ascent) + td (time of descent ) .

    [       Time of ascent is the time taken by the projectile to reach to max. height by the projectile. And time of descent is the time taken by the projectile to reach from highest position to the point on the ground .]

    As we know , for ascending motion , v = uy – gta

    But at highest point v=0 , so , 0= u sinθ – g ta

    g ta = u sinθ

    ta = u sinθ/g ;

    Hence, Time of flight  , T = 2 ta = 2u sinθ/g ……………eq.

     

    maximum height(H) – It is the maximum vertical height attained by the projectile above the point of projection during its flight .

    from 3rd equation of motion v2 -u2 =2as ;

    0 – u2sin2θ = – 2gH

    H = u2sin2θ/2g ……………………eq.

    Horizontal range(H) –  It is the displacement of the projectile  between point of projection and point of hitting the ground .

    Since there is no acceleration in horizontal direction and hence

    X= R = u cosθ x T = u cosθ . 2u sinθ/g = u2 2sinθ cosθ/g  = u2 sin2θ /g ;

    Range R = u2 sin2θ /g ………………eq.

    TO SEE THE COMPLETE VIDEO ON PROJECTILE GIVEN HORIZONTAL PROJECTION CLICK HERE-

    Velocity of projectile at any time –

    VELOCITY OF PROJECTILE AT ANY INSTANT
    VELOCITY OF PROJECTILE AT ANY INSTANT

    At ant time the velocity has two components vx (velocity along x- axis) and vy (velocity along y-axis ). So at any time velocity v= √vx2 + vy2

                                                                                           v = √ [u2 cos2 θ + (u sinθ – gt)2 ].

    Or , v = √ (u2 + g2t2-2ugt sinθ ).

    Let β be the angle of resultant velocity with horizontal direction then ,

    Tanβ = (u sinθ-gt) / (ucosθ)

    [ ***** note- question based on the projectile may be asked to find the all equations but angle of projection is θ with the vertical instead of  horizontal in that case  , at the place of sinθ take cosθ and vice-versa .*******]

  • What do you mean by Relative velocity ?

    What do you mean by Relative velocity ?

    This topic will discuss about the velocity of an object with respect to another object. In this article you will learn Relative Velocity Analysis  in both forms text and video as well.

     Relative velocity of one object with respect to another is the velocity with which one object moves with respect to another object .When two objects A and B are moving with different velocities , then the velocity of one object A with respect to another object B is called relative velocity of object A with respect to object B , hence relative velocity is defined as the time rate of change of relative position of one object with respect to another.

    • Watch Relative Velocity Analysis Video :

    Expression for the relative velocities – Suppose two objects A and B moving with uniform velocities VA and VB respectively along parallel straight line path in the

    (i) Same direction (I.e. angle between them is 00)  ;

    Relative velocity of A with respect to B = VA -(VB ) = VA -VB

     

    (ii) Opposite direction (I.e. angle between them is 1800)

    Relative velocity of A with respect to B = VA – (-VB ) = VA + VB

    To read or download complete topic of Relative velocity click here-

     

    Download QA for various chapters of Physics 

     

  • GRAPH

    GRAPH

    GRAPH

    In this post we will discuss about the graph , and how graphs makes to understand  the physics easily ?

    Graph-

    As we know it is not easy to study or understand the physics. Students who is taking interest in physics and want to understand the physics, it is necessary to improve your mathematics and most importantly graph, students who can’t solve the graphical questions will face lot of difficulties. So I am trying to provide some information/ knowledge for the students, so that students can understand the graphical questions easily. Now these days questions based on graph is important for every topics of physics specially the students who is appearing in the JEE/ NEET examination. Graph makes the calculation easier and it makes the topic to understand more easy. So every students must have to understand the graph and solve the questions based on it.

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  • MOTION

    MOTION

    MOTION

    MOTION , THERE DIFFERENT TYPES, AND EQUATIONS OF MOTION .

    MOTION OF AN OBJECT

     

    Motion –

    Rest and Motion -An object is said to be in rest , if body does not change its position with time , with respect to surroundings . An object is said to be in motion , if body  changes its position with time , with respect to surroundings .

    Motion of the body can be of following type –

    • Rectilinear / Translatory motion – In rectilinear motion a point mass body moves along a straight line . but in translator motion a body which is not a point mass moves in a straight line path.

     

    • Circular or rotatory motion – In circular motion a point mass object moves on a circular path. But in rotatory motion a body which is not a point mass moves on a circular path .

     

    • Oscillatory or vibratory motion– oscillatory motion is a type of motion in which a body moves to and fro or back and forth repeatedly about a fixed point. If in the oscillatory motion, amplitude is very small then the motion of the body is said to be in vibratory motion.

     

    Motion in one , two and three dimensions-

    • One dimensional motion– The motion of a body is said to be in one dimensional if only one co-ordinate specify the position of the object in the given time. In such a motion body moves along a straight line
    • Two dimensional motion– The motion of a body is said to be in two dimensional if any two coordinate specify the motion of the body.
    • Three dimensional motion – The motion of a body said to be in three dimensional if all three coordinates specify the motion of the body . in such kind of motion body may cover a specific motion or irregular motion.

     

    UNIFORM AND NON-UNIFORM MOTION- 

    Uniform motion – If a body covers equal distance in equal interval of time then it is said the motion of a body is uniform .

    Some important features of the uniform motion is following-

    (a) For a uniform motion  along a straight line in a given direction , the distance and magnitude of the displacement remain the same .

    (b) The velocity in uniform motion doesn’t depend upon the time interval .

    (c)There is no need of force for an object to be in uniform motion .

    (d) The velocity in uniform motion is in dependent of choice of origin.

    (e) The average and instantaneous velocities have value in uniform motion.

     

    If the motion of the object is uniform the following formula is used to find the

    different– different physical quantities .

     

    Distance = speed x time ;    speed = distance / time

     

    Displacement = velocity x time ;   Velocity = displacement / time ;

    Average speed = total distance covered / total time taken .

     

    Average velocity = total displacement covered / total time taken

     

    V =  X2-X1 / t2-t1 .

     

    Non-uniform motion- An object is said to be in non-uniform motion if it covers unequal distance in equal interval of time ,or equal distance in unequal interval of time. The velocity of a body changes with time it may increase ( accelerated ) or decrease (deaccelerate) with time .

    Following are the important equations of motion– for uniformly accelerated motion

    • 1st of motion ( it is also known as velocity – time relation)- v = u + at ( Where v=final velocity, u= initial velocity , a= acceleration, t = time taken .)
    • 2nd of motion (it also known as distance – time relation ) – S=ut+1/2 at2 (where s=displacement ;  u = initial velocity ; a= acceleration ; t = time taken .)
    • 3rd of motion (it is also known as the velocity- position relation) – V2-U2=2aS (where – S= displacement ; V= final velocity ; U= initial velocity ; a= acceleration .)

    TO SEE THE VIDEO FOR THE DERIVATION OF ALL THREE EQUATIONS OF MOTION CLICK HERE-

    • 4th of motion ( distance covered by the body in nth second ) Snth = u+ a(2n-1)/2 . (where Snth = distance covered in nth second ; a= acceleration ; n= given time ; u= initial velocity .)

    TO SEE THE VIDEO FOR THE DERIVATION OF 4th EQUATION OF MOTION CLICK HERE-

     

     To download  objective practice paper of motion in st line (akash)click here-

    the above assignment wiil be very helpful for the student preparing for NEET/ JEE and class 12-th board examination.

  • ADDITION OF VECTORS

    ADDITION OF VECTORS

    ADDITION OF VECTORS

    ADDITION OF VECTOR – Vectors can not be added by simple laws of algebra.

    Rules of geometric addition of vectors –

    • For the addition of two vectors – For the addition of two vectors represent these two vectors by arrowed lines using the same scale . Displace the second vector as its coincide with the head of first vector , then the single vector drawn from the tail of the first vector to the head of the second vector represent their resultant ( addition) vector.

    the addition of two vectors can be obtained using Triangle law or parallelogram law of vector addition

    • For the addition of three or more vectors – Represent these vectors by arrowed lines using the same scale . Displace these vectors such that the head of the first vector coincide with the tail of the second vector and head of second coincide with the tail of third vector and so on , then the single vector drawn from the tail of the first to the head of the last represent their resultant vector. The addition of three or more vectors can be found using polygon law of vector addition.

    Triangle law of vector addition-   It states that if two vectors acting on a particle represented by two sides of a triangle in same order , then the third side in opposite order gives the resultant vector.

    TO DOWNLOAD COMPLETE NOTES OF ADDITION OF VECTOR CLICK HERE-ADDITION OF VECTOR

  • What do you mean by the term vector quantity?

    What do you mean by the term vector quantity?

    What do you mean by the term vector quantity ?

    What do you mean by the term vector quantity? what are the uses of vector quantity? Explain different types of vector.

    VECTORS-

    Physical quantity having both magnitude and direction called vector quantity . And the physical quantity having magnitude only called scalar quantity . E.X.- suppose a man move 10 km , now in that case I am discussing about  its distance only i.e. it has magnitude only but there is no any information about its direction hence it is a scalar quantity, if we say man  is moving 10 km towards East(or any other direction ) so we can say we are discussing about its displacement i.e. it has both magnitude and direction. A vector quantity is represented as an arrow on its top ex;-  ? ⃗

    Vectors can be divided into two ways –

    • Polar vector- a vector which has a starting point or a point of application. E. X .- displacement , force etc.
    • (ii) Axial vector – Vectors which represent rotational effects and acts along the axis of rotation in accordance with right hand screw rule.

    TO DOWNLOAD VECTORS COMPLETE NOTES CLICK HERE.

     Addition of vectors (triangle law and parallelogram of vector addition)

  • DIMENSIONS

    DIMENSIONS

    DIMENSIONS

    What is dimensions of a physical quantity?What are the uses of dimensions ?

    DIMENSIONS– The dimension of a physical quantity as the power to which the fundamental units have to raised to represent a derived units of the quantity.

    To see the video of dimensions    click here

    As we know that derived units of the physical quantities can be obtained from fundamental units of mass , length and time . Fundamental unit of mass is represented as [M], length is represented as [L] , and time as [T] . If we have to derive the dimension of velocity , then it may be written as

    Velocity V = distance / time = [L] / [T] = [M0L1T-1] . Similarly we can find the dimensions of all physical quantities .

    The dimensions of the physical quantity is an expression which tells us : (i) The dimensional units on which the quantity depends and (ii) The nature of the dependence .

    The dimensional formula of a physical quantity can be obtained by defining there relation with other physical quantities , whose dimensions in mass, length and time are already known .

    When a physical quantity is equated to its dimensional formula , what we obtained is the dimensional equation of the physical quantity.

    Uses of dimensional equations : –

    • Checking the accuracy of formula ; Whether the given equations are correct or not can be checked on the basis of principle of homogeneity . according to this principle , the given formula is correct if dimension of left hand side of the equation is equal to the dimension of right hand side of a physical quantity.
    • To see the video of how to check the correctness of formula click here-
    • Conversion of one system of units into another ; – This is based on the fact that the magnitude of a physical quantity remains the same , whatever the system of its measurement. Q= n1u1 = n2u2. For to do that , we have to use the formula

    Which is given as , n2=n1 [M1/M2]a [L1/L2]b [T1/T2]c .

    To see the video on conversion of one system to another click here-

     Derivation of formula or to find the actual relationship between given physical quantities. Using the same principle of homogeneity of dimensions , we can derive the formula of physical quantity , provided we know the factors on which the physical quantity depends.

  • Errors of measurement

    Errors of measurement

    Errors of measurement-

    generally it is seen the measured value of a quantity is different from its actual value . this difference in the measured value and and the true value of a quantity is called error of measurement. 

    Errors of measurement can be divided into following types-

    Systematic errors -Those errors whose causes are known and it can be corrected ( or ,  can be minimised). Like Instrumental errors, personal errors ,Error due to imperfection and errors due to external causes.

    Random errors-These errors may arise due to large variety of factors . some time it is also called ‘ chance error’ . random errors can be minimised by repeating the observation.

    Gross errors– These errors arises due to carelessness of the observer during the measurement of the values.

    Absolute errors– Absolute errors in the measurement is the difference between true value and measured value of the quantities . The absolute errors sometime may be positive and sometime negative .

    Mean absolute error-It is the arithmetic mean of magnitudes of absolute errors.

    Relative errors /Fractional errors-It is the ratio of mean absolute errors to the mean value or true value of the quantities measured.

    Permissible errors-It is the errors which arises due to limitations on the measuring abilities of various instruments use in the experiment.

    Accuracy– It is the extent to which a measurement approaches the true value of the quantities measured.

    Precision– It describes the limitations of the measuring instruments . It is the degree of correctness of a measurement.

    To  download important questions  on Errors  click here

     

     

  • Significant figure

    Significant figure

    Significant figure

    In this topic we will discuss what is a significant figure ?  how can we find the significant figure in the given values and what are the rules for counting significant figure ?

    Significant figure – It is the measured value of a physical quantity tell the number of digit in which we are confident . (  Larger the value of significant figure greater will be the accuracy and vice versa ).

    Number of significant figure in a physical quantity depends upon the least count of the instrument used for its measurement.

    Rules for counting significant figure –

    1. All non zero digits are significant figure , and all zeros occurring between the two non zero digits  are significant.
    2. In a number less than 1 , all zeros to the right of decimal point and to the left of a nonzero digit are not significant . But all the zeros on the right of the last non zero digit in the decimal part are significant.
    3. All zeros on the right of non zero digits are not significant . but all zeros on the right of the last non zero becomes significant when they come from a measurement.

     

    (Note- change in the unit of measurement of a quantity does not change the number of significant figures .)