General
Easy
Physics-

A wire left parenthesis Y equals 2 cross times 10 to the power of 11 end exponent N m to the power of negative 2 end exponent right parenthesis has length 1 m and cross-sectional area 1 m m to the power of negative 2 end exponent. The work required to increase the length by 2 mm is

Physics-General

  1. 0.4 J    
  2. 4 J    
  3. 400 J    
  4. 40 J    

    Answer:The correct answer is: 0.4 JWork done = fraction numerator 1 over denominator 2 end fraction blank F increment l
    fraction numerator equals blank fraction numerator 1 over denominator 2 end fraction fraction numerator Y A increment l to the power of 2 end exponent over denominator l end fraction over denominator fraction numerator 2 cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 6 end exponent open parentheses 2 cross times 10 to the power of negative 3 end exponent close parentheses to the power of 2 end exponent over denominator 2 cross times 1 end fraction end fraction open vertical bar table row cell Y equals fraction numerator F l over denominator A increment l end fraction end cell row cell o r blank F equals fraction numerator Y A increment l over denominator l end fraction end cell end table close
    = 4cross times 10 to the power of negative 1 end exponent blank J equals 0.4 blank J

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    physics-

    The diagram shows a force-extension graph for a rubber band. Consider the following statements
    I. It will be easier to compress this rubber than expand it
    II. Rubber does not return to its original length after it is stretched
    III. The rubber band will get heated if it is stretched and released
    Which of these can be deduced from the graph

    Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating

    The diagram shows a force-extension graph for a rubber band. Consider the following statements
    I. It will be easier to compress this rubber than expand it
    II. Rubber does not return to its original length after it is stretched
    III. The rubber band will get heated if it is stretched and released
    Which of these can be deduced from the graph

    physics-General
    Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating
    General
    physics-

    The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is beta and the coefficient of volume expansion is alpha

    If coefficient of volume expansion is alpha and rise in temperature is increment theta then increment V equals V alpha increment theta rightwards double arrow fraction numerator increment V over denominator V end fraction equals alpha increment theta
    Volume elasticity beta equals fraction numerator P over denominator increment V divided by V end fraction equals fraction numerator P over denominator alpha increment theta end fraction rightwards double arrow increment theta equals fraction numerator P over denominator alpha beta end fraction

    The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is beta and the coefficient of volume expansion is alpha

    physics-General
    If coefficient of volume expansion is alpha and rise in temperature is increment theta then increment V equals V alpha increment theta rightwards double arrow fraction numerator increment V over denominator V end fraction equals alpha increment theta
    Volume elasticity beta equals fraction numerator P over denominator increment V divided by V end fraction equals fraction numerator P over denominator alpha increment theta end fraction rightwards double arrow increment theta equals fraction numerator P over denominator alpha beta end fraction
    General
    physics-

    Two magnets of equal mass are joined at 90degree each other as shown in figure. Magnet N subscript 1 end subscript S subscript 1 end subscript has a magnetic moment square root of 3 times that of N subscript 2 end subscript S subscript 2 end subscript. The arrangement is pivoted so that it is free to rotate in horizontal plane. When in equilibrium, what angle should N subscript 1 end subscript S subscript 1 end subscript make with magnetic meridian?

    In equilibrium, the resultant magnetic moment will be along magnetic meridian. Let N subscript 1 end subscript S subscript 1 end subscript make angle theta with resultant
    t a n theta equals fraction numerator M subscript 2 end subscript over denominator M subscript 1 end subscript end fraction equals fraction numerator M over denominator square root of 3 M end fraction equals fraction numerator 1 over denominator square root of 3 end fraction blank therefore theta equals 30 degree

    Two magnets of equal mass are joined at 90degree each other as shown in figure. Magnet N subscript 1 end subscript S subscript 1 end subscript has a magnetic moment square root of 3 times that of N subscript 2 end subscript S subscript 2 end subscript. The arrangement is pivoted so that it is free to rotate in horizontal plane. When in equilibrium, what angle should N subscript 1 end subscript S subscript 1 end subscript make with magnetic meridian?

    physics-General
    In equilibrium, the resultant magnetic moment will be along magnetic meridian. Let N subscript 1 end subscript S subscript 1 end subscript make angle theta with resultant
    t a n theta equals fraction numerator M subscript 2 end subscript over denominator M subscript 1 end subscript end fraction equals fraction numerator M over denominator square root of 3 M end fraction equals fraction numerator 1 over denominator square root of 3 end fraction blank therefore theta equals 30 degree
    General
    physics-

    Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance d from the center on the bisector of the right angle is

    Resolving the magnetic moments along O P and perpendicular toO P comma figure we find that component O P perpendicular O P cancel out. Resultant magnetic moment along O P i s equals M cos invisible function application 45 degree plus M c o s 45 degree

    equals 2 blank M c o s blank 45 degree equals fraction numerator 2 M over denominator square root of 2 end fraction equals square root of 2 M
    The point P lies on axial line of magnet of moment
    equals square root of 2 M
    therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 left parenthesis square root of 2 M right parenthesis over denominator d to the power of 3 end exponent end fraction

    Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance d from the center on the bisector of the right angle is

    physics-General
    Resolving the magnetic moments along O P and perpendicular toO P comma figure we find that component O P perpendicular O P cancel out. Resultant magnetic moment along O P i s equals M cos invisible function application 45 degree plus M c o s 45 degree

    equals 2 blank M c o s blank 45 degree equals fraction numerator 2 M over denominator square root of 2 end fraction equals square root of 2 M
    The point P lies on axial line of magnet of moment
    equals square root of 2 M
    therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 left parenthesis square root of 2 M right parenthesis over denominator d to the power of 3 end exponent end fraction
    General
    physics-

    A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

    Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
    equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
    Since for same material Young’s modulus is same, i e comma
    Y subscript 1 end subscript equals Y subscript 2 end subscript
    orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
    orl to the power of ´ end exponent equals l

    A wire of length Land radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2 a is stretched with a force 2F, the increase in its length will be

    physics-General
    Young’s modulus Y equals fraction numerator F L over denominator A l end fraction
    equals fraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction
    Since for same material Young’s modulus is same, i e comma
    Y subscript 1 end subscript equals Y subscript 2 end subscript
    orfraction numerator F L over denominator pi a to the power of 2 end exponent l end fraction equals fraction numerator open parentheses 2 F close parentheses left parenthesis 2 L right parenthesis over denominator pi open parentheses 2 a close parentheses to the power of 2 end exponent l ʹ end fraction
    orl to the power of ´ end exponent equals l
    General
    maths-

    y equals f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction comma x element of R comma y element of R text  is  end text

    y equals f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction comma x element of R comma y element of R text  is  end text

    maths-General
    General
    physics-

    The variation of intensity of magnetization left parenthesis I right parenthesis with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.

    For a dia-magnetic substance, I is negative and negative I proportional to H. Therefore, the variation is represented by O C o r O D. As magnetisation is small, O C is better choice.

    The variation of intensity of magnetization left parenthesis I right parenthesis with respect to the magnetizing field (H) in a diamagnetic substance is described by the graph in figure.

    physics-General
    For a dia-magnetic substance, I is negative and negative I proportional to H. Therefore, the variation is represented by O C o r O D. As magnetisation is small, O C is better choice.
    General
    physics-

    The Young’s modulus of the material of a wire is equal to the

    Young’s modulus of material Y equals fraction numerator L i n e a r blank s t r e s s over denominator L o n g i t u d i n a l blank s t r a i n end fraction
    If longitudinal strain is equal unity, then
    Y equals Linear stress produced

    The Young’s modulus of the material of a wire is equal to the

    physics-General
    Young’s modulus of material Y equals fraction numerator L i n e a r blank s t r e s s over denominator L o n g i t u d i n a l blank s t r a i n end fraction
    If longitudinal strain is equal unity, then
    Y equals Linear stress produced
    General
    maths-

    The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is

    n factorial

    The number of one one onto functions that can be defined from A={a,b,c,d} into B={1,2,3,4} is

    maths-General
    n factorial
    General
    physics-

    If the shear modulus of a wire material is 5.9blank cross times 10 to the power of 11 end exponent d y n e blank c m to the power of negative 2 end exponent then the potential energy of a wire of 4 cross times 10 to the power of 3 end exponent c m in diameter and 5 cm long twisted through an angle of 10’ , is

    To twist the wire through the angle d theta comma blankit is necessary to do the work
    d W equals blank tau d theta
    And theta equals 10 to the power of ´ end exponent equals fraction numerator 10 over denominator 60 end fraction cross times fraction numerator pi over denominator 180 end fraction equals fraction numerator pi over denominator 1080 end fraction r a d
    W equals blank not stretchy integral from 0 to theta of tau blank d theta equals blank not stretchy integral from 0 to theta of fraction numerator eta pi r to the power of 4 end exponent theta d theta over denominator 2 l end fraction equals blank fraction numerator eta pi r to the power of 4 end exponent theta over denominator 4 l end fraction
    W equals blank fraction numerator 5.9 blank cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 5 end exponent cross times blank pi open parentheses 2 cross times 10 to the power of negative 5 end exponent close parentheses to the power of 4 end exponent pi to the power of 2 end exponent over denominator 10 to the power of negative 4 end exponent cross times 4 cross times 5 cross times 10 to the power of negative 2 end exponent cross times open parentheses 1080 close parentheses to the power of 2 end exponent end fraction
    W equals 1.253 blank cross times 10 to the power of negative 12 end exponent blank J

    If the shear modulus of a wire material is 5.9blank cross times 10 to the power of 11 end exponent d y n e blank c m to the power of negative 2 end exponent then the potential energy of a wire of 4 cross times 10 to the power of 3 end exponent c m in diameter and 5 cm long twisted through an angle of 10’ , is

    physics-General
    To twist the wire through the angle d theta comma blankit is necessary to do the work
    d W equals blank tau d theta
    And theta equals 10 to the power of ´ end exponent equals fraction numerator 10 over denominator 60 end fraction cross times fraction numerator pi over denominator 180 end fraction equals fraction numerator pi over denominator 1080 end fraction r a d
    W equals blank not stretchy integral from 0 to theta of tau blank d theta equals blank not stretchy integral from 0 to theta of fraction numerator eta pi r to the power of 4 end exponent theta d theta over denominator 2 l end fraction equals blank fraction numerator eta pi r to the power of 4 end exponent theta over denominator 4 l end fraction
    W equals blank fraction numerator 5.9 blank cross times 10 to the power of 11 end exponent cross times 10 to the power of negative 5 end exponent cross times blank pi open parentheses 2 cross times 10 to the power of negative 5 end exponent close parentheses to the power of 4 end exponent pi to the power of 2 end exponent over denominator 10 to the power of negative 4 end exponent cross times 4 cross times 5 cross times 10 to the power of negative 2 end exponent cross times open parentheses 1080 close parentheses to the power of 2 end exponent end fraction
    W equals 1.253 blank cross times 10 to the power of negative 12 end exponent blank J
    General
    physics-

    The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law. P and Q represent

    Graph between applied force and extension will be straight line because in elastic range
    Applied force proportional to extension
    But the graph between extension and stored elastic energy will be parabolic in nature
    As U equals 1 divided by 2 blank k x to the power of 2 end exponent or U proportional to x to the power of 2 end exponent

    The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law. P and Q represent

    physics-General
    Graph between applied force and extension will be straight line because in elastic range
    Applied force proportional to extension
    But the graph between extension and stored elastic energy will be parabolic in nature
    As U equals 1 divided by 2 blank k x to the power of 2 end exponent or U proportional to x to the power of 2 end exponent
    General
    physics-

    A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

    Net elongation of the rod is

    l equals blank fraction numerator 3 F open parentheses fraction numerator 2 L over denominator 3 end fraction close parentheses over denominator A Y end fraction plus fraction numerator 2 F open parentheses fraction numerator L over denominator 3 end fraction close parentheses over denominator A Y end fraction
    l equals fraction numerator 8 F L over denominator 3 A Y end fraction

    A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

    physics-General
    Net elongation of the rod is

    l equals blank fraction numerator 3 F open parentheses fraction numerator 2 L over denominator 3 end fraction close parentheses over denominator A Y end fraction plus fraction numerator 2 F open parentheses fraction numerator L over denominator 3 end fraction close parentheses over denominator A Y end fraction
    l equals fraction numerator 8 F L over denominator 3 A Y end fraction
    General
    physics-

    A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

    Shearing strain = fraction numerator 0.02 blank cross times 10 to the power of negative 2 end exponent over denominator 0.1 blank end fraction equals 0.002

    A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

    physics-General
    Shearing strain = fraction numerator 0.02 blank cross times 10 to the power of negative 2 end exponent over denominator 0.1 blank end fraction equals 0.002
    General
    physics-

    A wire of length 2 L and radius r is stretched between A and B without the application of any tension. If Y is the Young’s modulus of the wire and it is stretched like A C B, then the tension in the wire will be

    T equals fraction numerator Y A l over denominator L end fraction
    Increase in length of one segment of wire
    l equals open parentheses L plus fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction close parentheses minus L equals fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction
    So, T equals fraction numerator Y pi r to the power of 2 end exponent. d to the power of 2 end exponent over denominator 2 L to the power of 2 end exponent end fraction

    A wire of length 2 L and radius r is stretched between A and B without the application of any tension. If Y is the Young’s modulus of the wire and it is stretched like A C B, then the tension in the wire will be

    physics-General
    T equals fraction numerator Y A l over denominator L end fraction
    Increase in length of one segment of wire
    l equals open parentheses L plus fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction close parentheses minus L equals fraction numerator 1 over denominator 2 end fraction fraction numerator d to the power of 2 end exponent over denominator L end fraction
    So, T equals fraction numerator Y pi r to the power of 2 end exponent. d to the power of 2 end exponent over denominator 2 L to the power of 2 end exponent end fraction
    General
    physics-

    The work done in deforming body is given by

    Let L be length of body, A the area of cross-section and l the increase in length.
    S t r e s s equals fraction numerator F over denominator A to the power of ´ end exponent end fraction s t r a i n equals fraction numerator l over denominator L end fraction
    Force necessary to deform the body is
    F equals fraction numerator Y A over denominator L end fraction l
    If body is deformed by a distance, then
    W o r k blank d o n e equals F cross times d l equals fraction numerator Y A over denominator L end fraction l d l
    W equals not stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator Y A over denominator L end fraction l d l equals fraction numerator Y A over denominator L end fraction open square brackets fraction numerator l to the power of 2 end exponent over denominator 2 end fraction close square brackets subscript 0 end subscript superscript l end superscript equals fraction numerator 1 over denominator 2 end fraction Y A fraction numerator l to the power of 2 end exponent over denominator L end fraction
    equals fraction numerator 1 over denominator 2 end fraction open parentheses Y fraction numerator l over denominator L end fraction close parentheses open parentheses fraction numerator l over denominator L end fraction close parentheses open parentheses A L close parentheses
    equals fraction numerator 1 over denominator 2 end fraction open parentheses s t r e s s cross times s t r a i n close parentheses cross times v o l u m e
    Hence, work done for unit volume is
    W equals fraction numerator 1 over denominator 2 end fraction s t r e s s cross times s r a i n.

    The work done in deforming body is given by

    physics-General
    Let L be length of body, A the area of cross-section and l the increase in length.
    S t r e s s equals fraction numerator F over denominator A to the power of ´ end exponent end fraction s t r a i n equals fraction numerator l over denominator L end fraction
    Force necessary to deform the body is
    F equals fraction numerator Y A over denominator L end fraction l
    If body is deformed by a distance, then
    W o r k blank d o n e equals F cross times d l equals fraction numerator Y A over denominator L end fraction l d l
    W equals not stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator Y A over denominator L end fraction l d l equals fraction numerator Y A over denominator L end fraction open square brackets fraction numerator l to the power of 2 end exponent over denominator 2 end fraction close square brackets subscript 0 end subscript superscript l end superscript equals fraction numerator 1 over denominator 2 end fraction Y A fraction numerator l to the power of 2 end exponent over denominator L end fraction
    equals fraction numerator 1 over denominator 2 end fraction open parentheses Y fraction numerator l over denominator L end fraction close parentheses open parentheses fraction numerator l over denominator L end fraction close parentheses open parentheses A L close parentheses
    equals fraction numerator 1 over denominator 2 end fraction open parentheses s t r e s s cross times s t r a i n close parentheses cross times v o l u m e
    Hence, work done for unit volume is
    W equals fraction numerator 1 over denominator 2 end fraction s t r e s s cross times s r a i n.