Physics
General
Easy
Question
The figure shows a system of two concentric spheres of radii and and kept at temperatures and respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

 In


The correct answer is:
To measure the radial rate of heat flow, we have to go for integration technique as here the area of the surface through which heat will flow is not constant.
Let us consider an element (spherical shell) of thickness d and radius as shown in figure. Let us first find the equivalent thermal resistance between inner and outer sphere.
Resistance of shell=
=
Rate of heat flow = H
=
=
Related Questions to study
maths
If the line y = x + 3 meets the circle at A and B, then equation of the circle on AB as diameter is
If the line y = x + 3 meets the circle at A and B, then equation of the circle on AB as diameter is
mathsGeneral
physics
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
and
An electric lamp is fixed at the ceiling of a circular tunnel as shown is figure. What is the ratio the intensities of light at base A and a point B on the wall
physicsGeneral
and
physics
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
The distance between a point source of light and a screen which is 60 cm is increased to 180 cm. The intensity on the screen as compared with the original intensity will be
physicsGeneral
Maths
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
Let the coordinates of the pole be (h, k).
The equation of the circle is 2x^{2} + 2y^{2}  3x + 5y  7 = 0.
Dividing both sides of the equation by 2,we get
x^{2} + y^{2}  3/2 x + 5/2 y  7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y  3/4 (x + h) + 5/4 (y+k)  7/2 = 0 .
Simplifying the equation, it can be written as (4h  3)x + (4k + 5)y + (3h + 5k  14).
We are given that the equation of the polar is 9x + y  28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h  3) /9 = (4k + 5) /1 = (3h + 5k  14) /28
Taking the first and third expression, we get
(4h  3) /9 = (3h + 5k  14) /28 .
By cross multiplication, we get
Or, 28 (4h  3) = 9 (3h + 5k  14)
Or, 112h + 84 = 27h + 45k  126
Or, 112h + 27h  45k = 126  84
Or, 85h  45k = 210
Or, 5 ( 17h + 9k ) = 210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( 3h + 5k  14) /28
By cross multiplication, we get
28 ( 4k + 5 ) = ( 3h + 5k  14 )
112k  140 = 3h + 5k  14
3h  112k  5k = 14 + 140
3h  117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = 1 .
Therefore, the coordinates are (3, 1) .
Hence, the correct option is (a).
The equation of the circle is 2x^{2} + 2y^{2}  3x + 5y  7 = 0.
Dividing both sides of the equation by 2,we get
x^{2} + y^{2}  3/2 x + 5/2 y  7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y  3/4 (x + h) + 5/4 (y+k)  7/2 = 0 .
Simplifying the equation, it can be written as (4h  3)x + (4k + 5)y + (3h + 5k  14).
We are given that the equation of the polar is 9x + y  28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h  3) /9 = (4k + 5) /1 = (3h + 5k  14) /28
Taking the first and third expression, we get
(4h  3) /9 = (3h + 5k  14) /28 .
By cross multiplication, we get
Or, 28 (4h  3) = 9 (3h + 5k  14)
Or, 112h + 84 = 27h + 45k  126
Or, 112h + 27h  45k = 126  84
Or, 85h  45k = 210
Or, 5 ( 17h + 9k ) = 210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( 3h + 5k  14) /28
By cross multiplication, we get
28 ( 4k + 5 ) = ( 3h + 5k  14 )
112k  140 = 3h + 5k  14
3h  112k  5k = 14 + 140
3h  117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = 1 .
Therefore, the coordinates are (3, 1) .
Hence, the correct option is (a).
The pole of the straight line 9x + y – 28 = 0 with respect to the circle is
MathsGeneral
Let the coordinates of the pole be (h, k).
The equation of the circle is 2x^{2} + 2y^{2}  3x + 5y  7 = 0.
Dividing both sides of the equation by 2,we get
x^{2} + y^{2}  3/2 x + 5/2 y  7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y  3/4 (x + h) + 5/4 (y+k)  7/2 = 0 .
Simplifying the equation, it can be written as (4h  3)x + (4k + 5)y + (3h + 5k  14).
We are given that the equation of the polar is 9x + y  28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h  3) /9 = (4k + 5) /1 = (3h + 5k  14) /28
Taking the first and third expression, we get
(4h  3) /9 = (3h + 5k  14) /28 .
By cross multiplication, we get
Or, 28 (4h  3) = 9 (3h + 5k  14)
Or, 112h + 84 = 27h + 45k  126
Or, 112h + 27h  45k = 126  84
Or, 85h  45k = 210
Or, 5 ( 17h + 9k ) = 210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( 3h + 5k  14) /28
By cross multiplication, we get
28 ( 4k + 5 ) = ( 3h + 5k  14 )
112k  140 = 3h + 5k  14
3h  112k  5k = 14 + 140
3h  117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = 1 .
Therefore, the coordinates are (3, 1) .
Hence, the correct option is (a).
The equation of the circle is 2x^{2} + 2y^{2}  3x + 5y  7 = 0.
Dividing both sides of the equation by 2,we get
x^{2} + y^{2}  3/2 x + 5/2 y  7/2 = 0.
The equation of polar for the point having coordinates (h, k) is
h x + k y  3/4 (x + h) + 5/4 (y+k)  7/2 = 0 .
Simplifying the equation, it can be written as (4h  3)x + (4k + 5)y + (3h + 5k  14).
We are given that the equation of the polar is 9x + y  28 = 0.so, the above equation and this equation represent the same line. Comparing the coefficient of the line, we get
(4h  3) /9 = (4k + 5) /1 = (3h + 5k  14) /28
Taking the first and third expression, we get
(4h  3) /9 = (3h + 5k  14) /28 .
By cross multiplication, we get
Or, 28 (4h  3) = 9 (3h + 5k  14)
Or, 112h + 84 = 27h + 45k  126
Or, 112h + 27h  45k = 126  84
Or, 85h  45k = 210
Or, 5 ( 17h + 9k ) = 210
17h + 9k = 42 . . . (1)
Taking the second and third expression, we get
(4k + 5) /1 = ( 3h + 5k  14) /28
By cross multiplication, we get
28 ( 4k + 5 ) = ( 3h + 5k  14 )
112k  140 = 3h + 5k  14
3h  112k  5k = 14 + 140
3h  117k = 126 . . . (2)
By solving equation (1) × 13 and equation (2) .
h = 3
By putting the value of h in equation (1) , we get
K = 1 .
Therefore, the coordinates are (3, 1) .
Hence, the correct option is (a).
physics
Three rods of equal length are joined to form an equilateral triangle O is the mid point of Distance remains same for small change in temperature. Coefficient of linear expansion for and is same, but that for is Then
Neglecting and
Three rods of equal length are joined to form an equilateral triangle O is the mid point of Distance remains same for small change in temperature. Coefficient of linear expansion for and is same, but that for is Then
physicsGeneral
Neglecting and
physics
A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?
A point source causes photoelectric effect from a small metal plate Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?
physicsGeneral
physics
One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
a)
b)
c)
One of the following figures respesents the variation of particle momentum with associated de Broglie wavelength
a)
b)
c)
physicsGeneral
physics
Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?
According to Newton’s law of cooling, rate of cooling is given by
Where c is specific heat of material.
or
rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
Where c is specific heat of material.
or
rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
Two circular discs A and B with equal radii are blackened. They are heated to some temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?
physicsGeneral
According to Newton’s law of cooling, rate of cooling is given by
Where c is specific heat of material.
or
rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
Where c is specific heat of material.
or
rate of cooling varies inversely as specific heat. From the graph, for A rate of cooling is larger. Therefore, specific heat of A is smaller.
physics
Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures
Hence graph between and will be a straight line with positive slope and negative intercept
Which of the curves in figure represents the relation between Celsius and Fahrenheit temperatures
physicsGeneral
Hence graph between and will be a straight line with positive slope and negative intercept
Maths
The area of circle centred at (1, 2) and passing through (4, 6) is
Here, we have to find the area of circle.
Now, the centre of circle is C (1, 2).
The circle passes through the point P(4, 6).
Radius = CP
= √(41) ^{2} + (62) ^{2}
= √(3) ^{2} + (4) ^{2}
= √9+16
=√25
=5
Therefore, radius is 5 unit.
Now, Area of circle = π × 5 ×5
= 25π .
Hence, the correct option is (a).
Now, the centre of circle is C (1, 2).
The circle passes through the point P(4, 6).
Radius = CP
= √(41) ^{2} + (62) ^{2}
= √(3) ^{2} + (4) ^{2}
= √9+16
=√25
=5
Therefore, radius is 5 unit.
Now, Area of circle = π × 5 ×5
= 25π .
Hence, the correct option is (a).
The area of circle centred at (1, 2) and passing through (4, 6) is
MathsGeneral
Here, we have to find the area of circle.
Now, the centre of circle is C (1, 2).
The circle passes through the point P(4, 6).
Radius = CP
= √(41) ^{2} + (62) ^{2}
= √(3) ^{2} + (4) ^{2}
= √9+16
=√25
=5
Therefore, radius is 5 unit.
Now, Area of circle = π × 5 ×5
= 25π .
Hence, the correct option is (a).
Now, the centre of circle is C (1, 2).
The circle passes through the point P(4, 6).
Radius = CP
= √(41) ^{2} + (62) ^{2}
= √(3) ^{2} + (4) ^{2}
= √9+16
=√25
=5
Therefore, radius is 5 unit.
Now, Area of circle = π × 5 ×5
= 25π .
Hence, the correct option is (a).
physics
Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities and . The points and are maintained at different temperatures for the heat to flow at the same rate along and then which of the following options is correct
The given arrangement of rods can be redrawn as follows
It is given that
It is given that
Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities and . The points and are maintained at different temperatures for the heat to flow at the same rate along and then which of the following options is correct
physicsGeneral
The given arrangement of rods can be redrawn as follows
It is given that
It is given that
physics
In the following diagram if then
In the following diagram if then
physicsGeneral
physics
The maximum kinetic energy (E_{k} ) of emitted photoelectrons against frequency v of incident radiation is plotted as shown in fig The slope of the graph is equal to
The maximum kinetic energy (E_{k} ) of emitted photoelectrons against frequency v of incident radiation is plotted as shown in fig The slope of the graph is equal to
physicsGeneral
maths
In centre of the triangle formed by the lines y = x, y = 3x and y = 8 – 3x is
In centre of the triangle formed by the lines y = x, y = 3x and y = 8 – 3x is
mathsGeneral
physics
A lamp rated at 100 cd hangs over the middle of a round table with diameter 3 m at a height of 2 m. It is replaced by a lamp of 25 cd and the distance to the table is changed so that the illumination at the centre of the table remains as before. The illumination at edge of the table becomes X times the original. Then X is
A lamp rated at 100 cd hangs over the middle of a round table with diameter 3 m at a height of 2 m. It is replaced by a lamp of 25 cd and the distance to the table is changed so that the illumination at the centre of the table remains as before. The illumination at edge of the table becomes X times the original. Then X is
physicsGeneral