Physics-
General
Easy

Question

A spherical shell of inner radius R subscript 1 end subscript, temperature T subscript 1 end subscript, outer radius R subscript 2 end subscriptand temperature T subscript 2 end subscript conducts heat current radailly. Let r be the distance of any point from the centre of the shell. For R subscript 1 end subscript less than r less than R subscript 2 end subscript, temperature T in the shell as a function of r can be expressed as T =

  1. fraction numerator open square brackets T subscript 1 end subscript R subscript 2 end subscript open parentheses r minus R subscript 1 end subscript close parentheses plus T subscript 2 end subscript R subscript 1 end subscript left parenthesis R subscript 2 end subscript minus r right parenthesis close square brackets over denominator R subscript 2 end subscript minus R subscript 1 end subscript end fraction    
  2. fraction numerator open square brackets T subscript 2 end subscript R subscript 2 end subscript open parentheses r minus R subscript 1 end subscript close parentheses plus T subscript 1 end subscript R subscript 1 end subscript left parenthesis R subscript 2 end subscript minus r right parenthesis close square brackets over denominator r open parentheses R subscript 2 end subscript minus R subscript 1 end subscript close parentheses end fraction    
  3. fraction numerator open square brackets T subscript 2 end subscript open parentheses r minus R subscript 1 end subscript close parentheses plus T subscript 1 end subscript left parenthesis R subscript 2 end subscript minus r right parenthesis close square brackets over denominator R subscript 2 end subscript minus R subscript 1 end subscript end fraction    
  4. open parentheses fraction numerator T subscript 1 end subscript plus T subscript 2 end subscript over denominator 2 end fraction close parentheses fraction numerator R subscript 1 end subscript R subscript 2 end subscript over denominator r to the power of 2 end exponent end fraction    

The correct answer is: fraction numerator open square brackets T subscript 2 end subscript R subscript 2 end subscript open parentheses r minus R subscript 1 end subscript close parentheses plus T subscript 1 end subscript R subscript 1 end subscript left parenthesis R subscript 2 end subscript minus r right parenthesis close square brackets over denominator r open parentheses R subscript 2 end subscript minus R subscript 1 end subscript close parentheses end fraction


    H equals fraction numerator left parenthesis T subscript 1 end subscript minus T subscript 2 end subscript right parenthesis 4 pi K R subscript 1 end subscript R subscript 2 end subscript over denominator R subscript 2 end subscript minus R subscript 1 end subscript end fraction equals fraction numerator left parenthesis T subscript 1 end subscript minus theta right parenthesis left parenthesis 4 pi K right parenthesis R subscript 1 end subscript r over denominator r minus R end fraction
    Solving “theta” can be obtained.

    Related Questions to study

    General
    physics-

     A certain mass of a gas is compressed first adiabatically [curve (a)], and then isothermally [curve (b)]. In both the cases, the initial state of the gas is same If W subscript 1 end subscript is the work done in the first case and W subscript 2 end subscript is the work done in the second case , then

     A certain mass of a gas is compressed first adiabatically [curve (a)], and then isothermally [curve (b)]. In both the cases, the initial state of the gas is same If W subscript 1 end subscript is the work done in the first case and W subscript 2 end subscript is the work done in the second case , then

    physics-General
    General
    physics-

    A resistance ‘R’ connected to an external battery is put inside an adiabatic cylinder containing an ideal gas as shown. The piston can move along cylinder length without friction and atmospheric pressure is P subscript 0 end subscript. The constant speed ‘v’ by which piston of area of cross-section A should be moved so that temperature of gas do not change is

    A resistance ‘R’ connected to an external battery is put inside an adiabatic cylinder containing an ideal gas as shown. The piston can move along cylinder length without friction and atmospheric pressure is P subscript 0 end subscript. The constant speed ‘v’ by which piston of area of cross-section A should be moved so that temperature of gas do not change is

    physics-General
    General
    physics-

    A curve graph showing the dependence of pressure and absolute temperature is obtained for an ideal gas, as shown for a certain process. In the given process

    A curve graph showing the dependence of pressure and absolute temperature is obtained for an ideal gas, as shown for a certain process. In the given process

    physics-General
    parallel
    General
    maths-

    If x equals e to the power of t end exponent sin invisible function application t comma blank y equals e to the power of t end exponent cos invisible function application t comma blank t h e n fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction blank a t blank x equals pi i s

    If x equals e to the power of t end exponent sin invisible function application t comma blank y equals e to the power of t end exponent cos invisible function application t comma blank t h e n fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction blank a t blank x equals pi i s

    maths-General
    General
    chemistry-

    In the process of extraction of gold, Roasted gold ore plus CN to the power of minus plus straight H subscript 2 straight O not stretchy ⟶ with straight O subscript 2 on top left square bracket x right square bracket plus OH to the power of minus semicolon left square bracket x right square bracket plus Z n not stretchy rightwards arrow left square bracket y right square bracket plus A u  [x] and [y] are:

    In the process of extraction of gold, Roasted gold ore plus CN to the power of minus plus straight H subscript 2 straight O not stretchy ⟶ with straight O subscript 2 on top left square bracket x right square bracket plus OH to the power of minus semicolon left square bracket x right square bracket plus Z n not stretchy rightwards arrow left square bracket y right square bracket plus A u  [x] and [y] are:

    chemistry-General
    General
    chemistry-

    Aqueous solution of F e S O subscript 4 end subscript gives test for both F e to the power of 2 plus end exponent and SO subscript 4 superscript 2 minus end superscript but after addition of excess of KCN, solution ceases to give test for F e to the power of 2 plus end exponent. This is due to the formation of

    Aqueous solution of F e S O subscript 4 end subscript gives test for both F e to the power of 2 plus end exponent and SO subscript 4 superscript 2 minus end superscript but after addition of excess of KCN, solution ceases to give test for F e to the power of 2 plus end exponent. This is due to the formation of

    chemistry-General
    parallel
    General
    physics-

    A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency 9 divided by pi rps. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes 37 to the power of ring operator end exponent the speed of the spot (a point) on the wall is:

    A light ray I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency 9 divided by pi rps. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes 37 to the power of ring operator end exponent the speed of the spot (a point) on the wall is:

    physics-General
    General
    physics-

    A plano concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be?

    A plano concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be?

    physics-General
    General
    physics-

    The figure shows a parallel slab of refractive index n subscript 2 end subscript which is surrounded by media of refractive indices n subscript 1 end subscript and n subscript 3 end subscript. Light is incident on the slab at angle of incidence theta left parenthesis not equal to 0 right parenthesis. The time taken by the ray to cross the slab is ' t subscript 1 end subscript blank to the power of ´ end exponent if incidence is from ' n subscript 1 end subscript ' and it is ' t subscript 2 end subscript ' if the incidence is from ' n subscript 3 end subscript '. Then assuming that n subscript 2 end subscript greater than n subscript 1 end subscript comma n subscript 2 end subscript greater than n subscript 3 end subscript and n subscript 3 end subscript greater than n subscript 1 end subscript, then value of t subscript 1 end subscript divided by t subscript 2 end subscript.

    The figure shows a parallel slab of refractive index n subscript 2 end subscript which is surrounded by media of refractive indices n subscript 1 end subscript and n subscript 3 end subscript. Light is incident on the slab at angle of incidence theta left parenthesis not equal to 0 right parenthesis. The time taken by the ray to cross the slab is ' t subscript 1 end subscript blank to the power of ´ end exponent if incidence is from ' n subscript 1 end subscript ' and it is ' t subscript 2 end subscript ' if the incidence is from ' n subscript 3 end subscript '. Then assuming that n subscript 2 end subscript greater than n subscript 1 end subscript comma n subscript 2 end subscript greater than n subscript 3 end subscript and n subscript 3 end subscript greater than n subscript 1 end subscript, then value of t subscript 1 end subscript divided by t subscript 2 end subscript.

    physics-General
    parallel
    General
    physics-

    Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB & CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces w.r.t. each other is:

    Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB & CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces w.r.t. each other is:

    physics-General
    General
    physics-

    In the figure shown, the image of a real object O is formed at point I. AB is the principal axis of the mirror. The mirror must be:

    In the figure shown, the image of a real object O is formed at point I. AB is the principal axis of the mirror. The mirror must be:

    physics-General
    General
    physics-

    A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray is incident from left, that is parallel to principal axis, exits parallel to the incident ray as shown in the figure. The refractive index n of the material of the cylinder is :

    A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray is incident from left, that is parallel to principal axis, exits parallel to the incident ray as shown in the figure. The refractive index n of the material of the cylinder is :

    physics-General
    parallel
    General
    chemistry-

    Which of the following statements are true (or) false -
    i) open square brackets Cr open parentheses NH subscript 3 close parentheses subscript 6 close square brackets open square brackets Cr left parenthesis CN right parenthesis subscript 6 close square brackets and open square brackets Cr open parentheses NH subscript 3 close parentheses subscript 4 left parenthesis CN right parenthesis subscript 2 close square brackets open square brackets Cr open parentheses NH subscript 3 close parentheses subscript 2 left parenthesis CN right parenthesis subscript 4 close square brackets are coordination isomers
    ii) open square brackets Cr left parenthesis py right parenthesis subscript 2 open parentheses straight H subscript 2 straight O close parentheses subscript 2 Cl subscript 2 close square brackets Cl and open square brackets Cr left parenthesis py right parenthesis subscript 2 open parentheses straight H subscript 2 straight O close parentheses Cl subscript 3 close square brackets straight H subscript 2 straight O are ionisation isomers
    iii) open square brackets Pt open parentheses NH subscript 3 close parentheses subscript 4 Br subscript 2 close square brackets Cl subscript 2 and open square brackets Pt open parentheses NH subscript 3 close parentheses subscript 4 Cl subscript 2 close square brackets Br subscript 2 are linkage isomers
    iv) cis platin exhibits geometrical isomerism

    Which of the following statements are true (or) false -
    i) open square brackets Cr open parentheses NH subscript 3 close parentheses subscript 6 close square brackets open square brackets Cr left parenthesis CN right parenthesis subscript 6 close square brackets and open square brackets Cr open parentheses NH subscript 3 close parentheses subscript 4 left parenthesis CN right parenthesis subscript 2 close square brackets open square brackets Cr open parentheses NH subscript 3 close parentheses subscript 2 left parenthesis CN right parenthesis subscript 4 close square brackets are coordination isomers
    ii) open square brackets Cr left parenthesis py right parenthesis subscript 2 open parentheses straight H subscript 2 straight O close parentheses subscript 2 Cl subscript 2 close square brackets Cl and open square brackets Cr left parenthesis py right parenthesis subscript 2 open parentheses straight H subscript 2 straight O close parentheses Cl subscript 3 close square brackets straight H subscript 2 straight O are ionisation isomers
    iii) open square brackets Pt open parentheses NH subscript 3 close parentheses subscript 4 Br subscript 2 close square brackets Cl subscript 2 and open square brackets Pt open parentheses NH subscript 3 close parentheses subscript 4 Cl subscript 2 close square brackets Br subscript 2 are linkage isomers
    iv) cis platin exhibits geometrical isomerism

    chemistry-General
    General
    physics-

    As shown in the figure the observer 'O' sees the distance AB as infinitely large. If refractive index of liquid is m1 and that of glass is mu subscript 2 end subscript comma text  then  end text fraction numerator mu subscript 1 end subscript over denominator mu subscript 2 end subscript end fraction text  is: end text

    As shown in the figure the observer 'O' sees the distance AB as infinitely large. If refractive index of liquid is m1 and that of glass is mu subscript 2 end subscript comma text  then  end text fraction numerator mu subscript 1 end subscript over denominator mu subscript 2 end subscript end fraction text  is: end text

    physics-General
    General
    physics-

    In the figure ABC is the cross section of a right angled prism and ACDE is the cross section of a glass slab. The value of theta so that light incident normally on the face AB does not cross the face AC is (given s i n to the power of negative 1 end exponent invisible function application left parenthesis 3 divided by 5 right parenthesis equals 37 to the power of ring operator end exponent)

    In the figure ABC is the cross section of a right angled prism and ACDE is the cross section of a glass slab. The value of theta so that light incident normally on the face AB does not cross the face AC is (given s i n to the power of negative 1 end exponent invisible function application left parenthesis 3 divided by 5 right parenthesis equals 37 to the power of ring operator end exponent)

    physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.