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# CBSE Solved Paper 1 : Physical World Class 11 Notes | EduRev

## Class 11 : CBSE Solved Paper 1 : Physical World Class 11 Notes | EduRev

``` Page 1

Solved Paper-5
Class 11, Physics

Time: 3 hours         Max. Marks 70
General Instructions
1.  All questions are compulsory. Symbols have their usual meaning.
2.  Use of calculator is not permitted. However you may use log table, if required.
4.  Q.No. 1 to 7 are of very short answer type questions, carrying 1 mark each.
5.  Q.No.8 to 19 are of short answer type questions, carrying 2 marks each.
6.  Q. No. 20 to 27 carry 3 marks each. Q. No. 28 to 30 carry 5 marks each.

1.  Arrange four fundamental forces in decreasing order of strength.
2.  State the number of significant figures in the following:
(a)  0.007 m
2

(b)  2.64 × 10
24
kg

3.  Draw Velocity–time graph for motions with positive constant acceleration in
positive Direction.

4.  For what value of a does the vectors
ˆ ˆ ˆ
2 A ai j k = - +

and
ˆ ˆ ˆ
2 4 B ai aj k = + - 
are
perpendicular to each other.

5.  The casing of a rocket in flight burns up due to friction. At whose expense is the
heat energy required for burning obtained? The rocket or the atmosphere?

6.  Give the location of the centre of mass of a cube of uniform mass density

7.  There were two fixed points in the original Celsius scale as mentioned above which
were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one
of the fixed points is the triple-point of water, which on the Kelvin absolute scale is
assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?

8.  We measure the period of oscillation of a simple pendulum. In successive
measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s.
Calculate the absolute errors, relative error or percentage error.

Page 2

Solved Paper-5
Class 11, Physics

Time: 3 hours         Max. Marks 70
General Instructions
1.  All questions are compulsory. Symbols have their usual meaning.
2.  Use of calculator is not permitted. However you may use log table, if required.
4.  Q.No. 1 to 7 are of very short answer type questions, carrying 1 mark each.
5.  Q.No.8 to 19 are of short answer type questions, carrying 2 marks each.
6.  Q. No. 20 to 27 carry 3 marks each. Q. No. 28 to 30 carry 5 marks each.

1.  Arrange four fundamental forces in decreasing order of strength.
2.  State the number of significant figures in the following:
(a)  0.007 m
2

(b)  2.64 × 10
24
kg

3.  Draw Velocity–time graph for motions with positive constant acceleration in
positive Direction.

4.  For what value of a does the vectors
ˆ ˆ ˆ
2 A ai j k = - +

and
ˆ ˆ ˆ
2 4 B ai aj k = + - 
are
perpendicular to each other.

5.  The casing of a rocket in flight burns up due to friction. At whose expense is the
heat energy required for burning obtained? The rocket or the atmosphere?

6.  Give the location of the centre of mass of a cube of uniform mass density

7.  There were two fixed points in the original Celsius scale as mentioned above which
were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one
of the fixed points is the triple-point of water, which on the Kelvin absolute scale is
assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?

8.  We measure the period of oscillation of a simple pendulum. In successive
measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s.
Calculate the absolute errors, relative error or percentage error.

9.  An aircraft is flying at a height of 3400 m above the ground. If the angle subtended
at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the
speed of the aircraft?

10.  A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the
shell is 80 ms
–1
, what is the recoil speed of the gun?

11.  The speed-time graph of a particle moving along a fixed direction is shown in Fig.
Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to
6 s.

What is the average speed of the particle over the intervals in (a) and (b)?

12.  A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s
–1
.
The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the
rotation of the cylinder? What is the magnitude of angular momentum of the

13.  A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls
with decreasing acceleration (due to viscous resistance of the air) until at half its
original height, it attains its maximum (terminal) speed, and moves with uniform
speed thereafter. What is the work done by the gravitational force on the drop in the
first and second half of its journey? What is the work done by the resistive force in
the entire journey if its speed on reaching the ground is 10 m s
–1
?
14.  Two wires of diameter 0.25 cm, one made of steel and the other made of brass are
loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of
brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.

Page 3

Solved Paper-5
Class 11, Physics

Time: 3 hours         Max. Marks 70
General Instructions
1.  All questions are compulsory. Symbols have their usual meaning.
2.  Use of calculator is not permitted. However you may use log table, if required.
4.  Q.No. 1 to 7 are of very short answer type questions, carrying 1 mark each.
5.  Q.No.8 to 19 are of short answer type questions, carrying 2 marks each.
6.  Q. No. 20 to 27 carry 3 marks each. Q. No. 28 to 30 carry 5 marks each.

1.  Arrange four fundamental forces in decreasing order of strength.
2.  State the number of significant figures in the following:
(a)  0.007 m
2

(b)  2.64 × 10
24
kg

3.  Draw Velocity–time graph for motions with positive constant acceleration in
positive Direction.

4.  For what value of a does the vectors
ˆ ˆ ˆ
2 A ai j k = - +

and
ˆ ˆ ˆ
2 4 B ai aj k = + - 
are
perpendicular to each other.

5.  The casing of a rocket in flight burns up due to friction. At whose expense is the
heat energy required for burning obtained? The rocket or the atmosphere?

6.  Give the location of the centre of mass of a cube of uniform mass density

7.  There were two fixed points in the original Celsius scale as mentioned above which
were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one
of the fixed points is the triple-point of water, which on the Kelvin absolute scale is
assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?

8.  We measure the period of oscillation of a simple pendulum. In successive
measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s.
Calculate the absolute errors, relative error or percentage error.

9.  An aircraft is flying at a height of 3400 m above the ground. If the angle subtended
at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the
speed of the aircraft?

10.  A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the
shell is 80 ms
–1
, what is the recoil speed of the gun?

11.  The speed-time graph of a particle moving along a fixed direction is shown in Fig.
Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to
6 s.

What is the average speed of the particle over the intervals in (a) and (b)?

12.  A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s
–1
.
The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the
rotation of the cylinder? What is the magnitude of angular momentum of the

13.  A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls
with decreasing acceleration (due to viscous resistance of the air) until at half its
original height, it attains its maximum (terminal) speed, and moves with uniform
speed thereafter. What is the work done by the gravitational force on the drop in the
first and second half of its journey? What is the work done by the resistive force in
the entire journey if its speed on reaching the ground is 10 m s
–1
?
14.  Two wires of diameter 0.25 cm, one made of steel and the other made of brass are
loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of
brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.

15.  A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and
then placed on a large ice block. What is the maximum amount of ice that can melt?
(Specific heat of copper = 0.39 J g
–1
K
–1
; heat of fusion of water = 335 J g
–1
).

16.  In changing the state of a gas adiabatically from an equilibrium state A to another
equilibrium stateB, an amount of work equal to 22.3 J is done on the system. If the
gas is taken from state A to B via a process in which the net heat absorbed by the
system is 9.35 cal, how much is the net work done by the system in the latter case?
(Take 1 cal = 4.19 J)

17.  What amount of heat must be supplied to 2.0 × 10
–2
kg of nitrogen (at room
temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass
of N
2
= 28; R = 8.3 J mol
–1
K
–1
.)
18.  Explain why
(a)  To keep a piece of paper horizontal, you should blow over, not under, it
(b)  When we try to close a water tap with our fingers, fast jets of water gush
through the openings between our fingers

19.  Let us assume that our galaxy consists of 2.5 × 10
11
stars each of one solar mass.
How long will a star at a distance of 50,000 ly from the galactic centre take to
complete one revolution? Take the diameter of the Milky Way to be 10
5
ly.

20.  A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s
–1
to
3.5 m s
–1
in 25 s. The direction of the motion of the body remains unchanged. What
is the magnitude and direction of the force?

21.  The position of a particle is given by

Where t is in seconds and the coefficients have the proper units for r to be in metres.
(a)  Find the v and a of the particle?
(b)  What is the magnitude and direction of velocity of the particle at t = 2.0 s?

22.  The oxygen molecule has a mass of 5.30 × 10
–26
kg and a moment of inertia
of 1.94×10
–46
kg m
2
about an axis through its centre perpendicular to the lines
joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500
m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of
translation. Find the average angular velocity of the molecule.

Page 4

Solved Paper-5
Class 11, Physics

Time: 3 hours         Max. Marks 70
General Instructions
1.  All questions are compulsory. Symbols have their usual meaning.
2.  Use of calculator is not permitted. However you may use log table, if required.
4.  Q.No. 1 to 7 are of very short answer type questions, carrying 1 mark each.
5.  Q.No.8 to 19 are of short answer type questions, carrying 2 marks each.
6.  Q. No. 20 to 27 carry 3 marks each. Q. No. 28 to 30 carry 5 marks each.

1.  Arrange four fundamental forces in decreasing order of strength.
2.  State the number of significant figures in the following:
(a)  0.007 m
2

(b)  2.64 × 10
24
kg

3.  Draw Velocity–time graph for motions with positive constant acceleration in
positive Direction.

4.  For what value of a does the vectors
ˆ ˆ ˆ
2 A ai j k = - +

and
ˆ ˆ ˆ
2 4 B ai aj k = + - 
are
perpendicular to each other.

5.  The casing of a rocket in flight burns up due to friction. At whose expense is the
heat energy required for burning obtained? The rocket or the atmosphere?

6.  Give the location of the centre of mass of a cube of uniform mass density

7.  There were two fixed points in the original Celsius scale as mentioned above which
were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one
of the fixed points is the triple-point of water, which on the Kelvin absolute scale is
assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?

8.  We measure the period of oscillation of a simple pendulum. In successive
measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s.
Calculate the absolute errors, relative error or percentage error.

9.  An aircraft is flying at a height of 3400 m above the ground. If the angle subtended
at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the
speed of the aircraft?

10.  A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the
shell is 80 ms
–1
, what is the recoil speed of the gun?

11.  The speed-time graph of a particle moving along a fixed direction is shown in Fig.
Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to
6 s.

What is the average speed of the particle over the intervals in (a) and (b)?

12.  A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s
–1
.
The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the
rotation of the cylinder? What is the magnitude of angular momentum of the

13.  A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls
with decreasing acceleration (due to viscous resistance of the air) until at half its
original height, it attains its maximum (terminal) speed, and moves with uniform
speed thereafter. What is the work done by the gravitational force on the drop in the
first and second half of its journey? What is the work done by the resistive force in
the entire journey if its speed on reaching the ground is 10 m s
–1
?
14.  Two wires of diameter 0.25 cm, one made of steel and the other made of brass are
loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of
brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.

15.  A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and
then placed on a large ice block. What is the maximum amount of ice that can melt?
(Specific heat of copper = 0.39 J g
–1
K
–1
; heat of fusion of water = 335 J g
–1
).

16.  In changing the state of a gas adiabatically from an equilibrium state A to another
equilibrium stateB, an amount of work equal to 22.3 J is done on the system. If the
gas is taken from state A to B via a process in which the net heat absorbed by the
system is 9.35 cal, how much is the net work done by the system in the latter case?
(Take 1 cal = 4.19 J)

17.  What amount of heat must be supplied to 2.0 × 10
–2
kg of nitrogen (at room
temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass
of N
2
= 28; R = 8.3 J mol
–1
K
–1
.)
18.  Explain why
(a)  To keep a piece of paper horizontal, you should blow over, not under, it
(b)  When we try to close a water tap with our fingers, fast jets of water gush
through the openings between our fingers

19.  Let us assume that our galaxy consists of 2.5 × 10
11
stars each of one solar mass.
How long will a star at a distance of 50,000 ly from the galactic centre take to
complete one revolution? Take the diameter of the Milky Way to be 10
5
ly.

20.  A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s
–1
to
3.5 m s
–1
in 25 s. The direction of the motion of the body remains unchanged. What
is the magnitude and direction of the force?

21.  The position of a particle is given by

Where t is in seconds and the coefficients have the proper units for r to be in metres.
(a)  Find the v and a of the particle?
(b)  What is the magnitude and direction of velocity of the particle at t = 2.0 s?

22.  The oxygen molecule has a mass of 5.30 × 10
–26
kg and a moment of inertia
of 1.94×10
–46
kg m
2
about an axis through its centre perpendicular to the lines
joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500
m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of
translation. Find the average angular velocity of the molecule.

23.  Two inclined frictionless tracks, one gradual and
the other steep meet at A from where two stones
are allowed to slide down from rest, one on each
track. Will the stones reach the bottom at the
same time? Will they reach there with the same
speed? Explain. Given ?
1
= 30°, ?
2
= 60°, andh =
10 m, what are the speeds and times taken by the
two stones?
24.  A brass boiler has a base area of 0.15 m
2
and thickness 1.0 cm. It boils water at the
rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part
of the flame in contact with the boiler. Thermal conductivity of brass = 109 J s
–1
m
–
1
K
–1
; Heat of vaporisation of water = 2256 × 10
3
J kg
–1
.
(a)  Time period of a particle in SHM depends on the force constant k and
mass m of the particle:
. A simple pendulum executes SHM approximately. Why then is the
time period of a pendulum independent of the mass of the pendulum?
(b)  The motion of a simple pendulum is approximately simple harmonic for small
angle oscillations. For larger angles of oscillation, a more involved analysis
shows that T is greater than . Think of a qualitative argument to
appreciate this result.
(c)  A man with a wristwatch on his hand falls from the top of a tower. Does the
watch give correct time during the free fall?
(d)  What is the frequency of oscillation of a simple pendulum mounted in a
cabinthat is freely falling under gravity?

26.  Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-
tube open at both ends. If the U-tube contains water, what is the difference in its
levels in the two limbs of the tube? Surface tension of water at the temperature of
the experiment is 7.3 × 10
–2
N m
–1
. Take the angle of contact to be zero and density
of water to be 1.0 × 10
3
kg m
–3
(g = 9.8 m s
–2
).

27.  A spaceship is stationed on Mars. How much energy must be expended on the
spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg;
mass of the Sun = 2 × 10
30
kg; mass of mars = 6.4 × 10
23
kg; radius of mars = 3395
km; radius of the orbit of mars = 2.28 × 10
8
kg; G= 6.67 × 10
–11
m
2
kg
–2
.

Page 5

Solved Paper-5
Class 11, Physics

Time: 3 hours         Max. Marks 70
General Instructions
1.  All questions are compulsory. Symbols have their usual meaning.
2.  Use of calculator is not permitted. However you may use log table, if required.
4.  Q.No. 1 to 7 are of very short answer type questions, carrying 1 mark each.
5.  Q.No.8 to 19 are of short answer type questions, carrying 2 marks each.
6.  Q. No. 20 to 27 carry 3 marks each. Q. No. 28 to 30 carry 5 marks each.

1.  Arrange four fundamental forces in decreasing order of strength.
2.  State the number of significant figures in the following:
(a)  0.007 m
2

(b)  2.64 × 10
24
kg

3.  Draw Velocity–time graph for motions with positive constant acceleration in
positive Direction.

4.  For what value of a does the vectors
ˆ ˆ ˆ
2 A ai j k = - +

and
ˆ ˆ ˆ
2 4 B ai aj k = + - 
are
perpendicular to each other.

5.  The casing of a rocket in flight burns up due to friction. At whose expense is the
heat energy required for burning obtained? The rocket or the atmosphere?

6.  Give the location of the centre of mass of a cube of uniform mass density

7.  There were two fixed points in the original Celsius scale as mentioned above which
were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one
of the fixed points is the triple-point of water, which on the Kelvin absolute scale is
assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale ?

8.  We measure the period of oscillation of a simple pendulum. In successive
measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s.
Calculate the absolute errors, relative error or percentage error.

9.  An aircraft is flying at a height of 3400 m above the ground. If the angle subtended
at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the
speed of the aircraft?

10.  A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the
shell is 80 ms
–1
, what is the recoil speed of the gun?

11.  The speed-time graph of a particle moving along a fixed direction is shown in Fig.
Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to
6 s.

What is the average speed of the particle over the intervals in (a) and (b)?

12.  A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s
–1
.
The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the
rotation of the cylinder? What is the magnitude of angular momentum of the

13.  A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls
with decreasing acceleration (due to viscous resistance of the air) until at half its
original height, it attains its maximum (terminal) speed, and moves with uniform
speed thereafter. What is the work done by the gravitational force on the drop in the
first and second half of its journey? What is the work done by the resistive force in
the entire journey if its speed on reaching the ground is 10 m s
–1
?
14.  Two wires of diameter 0.25 cm, one made of steel and the other made of brass are
loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of
brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.

15.  A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and
then placed on a large ice block. What is the maximum amount of ice that can melt?
(Specific heat of copper = 0.39 J g
–1
K
–1
; heat of fusion of water = 335 J g
–1
).

16.  In changing the state of a gas adiabatically from an equilibrium state A to another
equilibrium stateB, an amount of work equal to 22.3 J is done on the system. If the
gas is taken from state A to B via a process in which the net heat absorbed by the
system is 9.35 cal, how much is the net work done by the system in the latter case?
(Take 1 cal = 4.19 J)

17.  What amount of heat must be supplied to 2.0 × 10
–2
kg of nitrogen (at room
temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass
of N
2
= 28; R = 8.3 J mol
–1
K
–1
.)
18.  Explain why
(a)  To keep a piece of paper horizontal, you should blow over, not under, it
(b)  When we try to close a water tap with our fingers, fast jets of water gush
through the openings between our fingers

19.  Let us assume that our galaxy consists of 2.5 × 10
11
stars each of one solar mass.
How long will a star at a distance of 50,000 ly from the galactic centre take to
complete one revolution? Take the diameter of the Milky Way to be 10
5
ly.

20.  A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s
–1
to
3.5 m s
–1
in 25 s. The direction of the motion of the body remains unchanged. What
is the magnitude and direction of the force?

21.  The position of a particle is given by

Where t is in seconds and the coefficients have the proper units for r to be in metres.
(a)  Find the v and a of the particle?
(b)  What is the magnitude and direction of velocity of the particle at t = 2.0 s?

22.  The oxygen molecule has a mass of 5.30 × 10
–26
kg and a moment of inertia
of 1.94×10
–46
kg m
2
about an axis through its centre perpendicular to the lines
joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500
m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of
translation. Find the average angular velocity of the molecule.

23.  Two inclined frictionless tracks, one gradual and
the other steep meet at A from where two stones
are allowed to slide down from rest, one on each
track. Will the stones reach the bottom at the
same time? Will they reach there with the same
speed? Explain. Given ?
1
= 30°, ?
2
= 60°, andh =
10 m, what are the speeds and times taken by the
two stones?
24.  A brass boiler has a base area of 0.15 m
2
and thickness 1.0 cm. It boils water at the
rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part
of the flame in contact with the boiler. Thermal conductivity of brass = 109 J s
–1
m
–
1
K
–1
; Heat of vaporisation of water = 2256 × 10
3
J kg
–1
.
(a)  Time period of a particle in SHM depends on the force constant k and
mass m of the particle:
. A simple pendulum executes SHM approximately. Why then is the
time period of a pendulum independent of the mass of the pendulum?
(b)  The motion of a simple pendulum is approximately simple harmonic for small
angle oscillations. For larger angles of oscillation, a more involved analysis
shows that T is greater than . Think of a qualitative argument to
appreciate this result.
(c)  A man with a wristwatch on his hand falls from the top of a tower. Does the
watch give correct time during the free fall?
(d)  What is the frequency of oscillation of a simple pendulum mounted in a
cabinthat is freely falling under gravity?

26.  Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-
tube open at both ends. If the U-tube contains water, what is the difference in its
levels in the two limbs of the tube? Surface tension of water at the temperature of
the experiment is 7.3 × 10
–2
N m
–1
. Take the angle of contact to be zero and density
of water to be 1.0 × 10
3
kg m
–3
(g = 9.8 m s
–2
).

27.  A spaceship is stationed on Mars. How much energy must be expended on the
spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg;
mass of the Sun = 2 × 10
30
kg; mass of mars = 6.4 × 10
23
kg; radius of mars = 3395
km; radius of the orbit of mars = 2.28 × 10
8
kg; G= 6.67 × 10
–11
m
2
kg
–2
.

28.  A thin circular loop of radius R rotates about its vertical diameter with an angular
frequency ?. Show that a small bead on the wire loop remains at its lowermost point
for .What is the angle made by the radius vector joining the centre to the
bead with the vertical downward direction for ?Neglect friction.

29.  (i)  A metre-long tube open at one end, with a movable piston at the other end,
shows resonance with a fixed frequency source (a tuning fork of frequency 340
Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in
air at the temperature of the experiment. The edge effects may be neglected.
(ii)  You have learnt that a travelling wave in one dimension is represented by a
function y = f (x, t)wherex and t must appear in the combination x – v t or x + v
t, i.e. y = f (x ± v t). Is the converse true? Examine if the following functions
for y can possibly represent a travelling wave:
(a)  (x – vt)
2

(b)
(c)

30.  A gas in equilibrium has uniform density and pressure throughout its volume. This
is strictly true only if there are no external influences. A gas column under gravity,
for example, does not have uniform density (and pressure). As you might expect, its
density decreases with height. The precise dependence is given by the so-called law
of atmospheres
n
2
= n
1
exp [-mg (h
2
– h
1
)/ k
B
T]
Where n
2
, n
1
refer to number density at heights h
2
and h
1
respectively. Use this
relation to derive the equation for sedimentation equilibrium of a suspension in a
liquid column:
n
2
= n
1
exp [-mg N
A
(? - P') (h
2
–h
1
)/ (?RT)]
Where ? is the density of the suspended particle, and ?’ that of surrounding medium.
[N
A
is Avogadro’s number, and R the universal gas constant.] [Hint: Use
Archimedes principle to find the apparent weight of the suspended particle.]

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