Question bank on kinematics

testybelchMechanics

Nov 14, 2013 (3 years and 9 months ago)

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CLASS
-

XI PHYSICS

Question bank on kinematics






( 1 mark questions)


Q1. Define frame of reference?

Q2. Define displacement?

Q3. What is the nature of position
-
time graph of a stationary object?

Q4. What is the nature of position
-
time graph in uniform

motion?

Q5. What does the slope of position
-
time graph represent?

Q6. What does the area under position
-
time graph represent?

Q7. What does the area under velocity
-
time graph represent?

Q8. What does the slope of velocity
-
time graph represent?

Q9. Define
relative velocity in one dimension?

Q10. If an object goes from A to B and cover a distance of 20 cm then again go from B to A. then what is
the total distance and total displacement of the object?

Q11. If x=5t
2

+7t+3m, then find velocity at t=2sec, where
x is the displacement?

Q12. What do you mean by vector quantity?

Q13. What is difference between position and displacement vector?

Q14. What is the statement of triangle law of vector addition?

Q15. What is the statement of parallelogram law of vector addi
tion?

Q16. What do you mean by resolution of vectors?

Q17. What do you mean by rectangular component of vectors?

Q18. Define a projectile?

Q19. Define trajectory?

Q20. Give an example of motion of particle which has constant speed but have acceleration?


( 2 mark questions)

Q1
-
If in case of motion displacement is directly proportional to the square of time elapsed, what do you
think about its acceleration' Explain ,why?

Q2Which graph represents higher velocity and why?



x


t

Q3 An object is moving w
ith constant velocity v along a straight line. What will be the shape of
displacement
-
time graph if

(a)x
o
=
-
ve, v=+ve (b)x
0
=+ve v=
-
ve

Q4 The minutes hand of a wall clock is 10 cm long. Find its displacement and the distance covered from
12.00 noon t
o 12.30pm

Q5 A particle is thrown upwards. It attains a height h after 5 s and again after 9 s. What is the speed of
the particle at height h?

Q6 Find the angle between two vectors




and




if resultant of two vectors is given by R
2
=P
2

+Q
2
.

Q7 One of th
e rectangular components of a velocity of 60km/h is 30 km/h.Find the other rectangular
component.

Q8 A car travels 20 km due north and then 35km in a direction 60
o
west of north. Find the magnitude
and direction of resultant displacement of the car.

Q9 Fin
d a unit vector parallel to the vector





̂



̂



̂
.

Q10 Show that the maximum horizontal range of a projectile is four times the corresponding maximum
height.


Q11 A train is moving due east with a velocity of 60km/h and a car is running due north with
a velocity
of 60km/h.What is the observed velocity of the car as felt by a passenger in the train.


Q12 Prove that A= I
-

2J AND B=2i + j are mutually perpendicular to each other.

Q13 A swimmer can swim with velocity of 10 km/h with respect the wate
r floing in a river with
velocity of 5km/h. In what direction should he swim to reach the point on the other bank just opposite
to hi starting point.?

QA14 Earth moves in circular orbit around the sun once every year with an orbital radius of 1,5x10
11

m.

What is the acceleration of earth towards the centre f the sun?

Q15 Define uniform circular motion. Is it an accelerated motion ? If yes ,what is the direction of the
acceleration?






( 3 mark questions)

Q.1 A

ball is thrown vertically upward with a velocity of 20m/sec from top of a multistoried building. The
height of a point from where the ball is thrown is 25 m from the ground. (i) how high the ball will rise?
(ii) How long will it be before the ball hit th
e ground?

Q 2. show that the area under velocity

time graph of an object moving with constant acceleration in a
straight line in a certain time interval is equal to the distance covered by the object in that interval.

Q 3. use integration technique to pr
ove that the distance travelled in nth second,

S
nth

= u+










Q 4.

Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle
moving with uniform speed v along a circular path of radius r. Discuss the direction of this acceleration.

Q 5. A man can swim with a speed of 4km/h in a
still water. How long does he take to cross the river
1km wide, if the river flows steadily at 3km/h and he makes his stroke normal to the water current? How
far from the river does he go, when he reaches the other bank?

Q6.A stone is tied to the end of a
string 80cm along is whirled in a horizontal circle with a constant
speed. If the stone makes14 revolutions in 25 secs, what is the magnitude and direction of a
acceleration of the stone?



Q7. The resultant of two vectors




and




is perpendicular to




and its magnitude is half that of



. What
is the angle between vectors




and



?

Q8.Draw Velocity time graph for uniformly accelerated motion . Show that slope of velocity v time graph
gives acceleration of the body.

Q9.Define relative velocity of one o
bject w.r.t another object draw position time graphs for two objects
moving along straight line when their relative velocity is (i) Zero (ii) Positive (iii) Negative.

Q10.

Two balls are thrown simultaneously , A vertically upward with speed of 20 m/s from

the ground
,and B vertically downwards form a height of 40m with the same speed and along the same line of
motion .At what points do the two balls collide? G= 9.8 m/s
2

.

Q1
1
.Define centripetal acceleration & hence derive expression for it?

(5 mark questi
ons)

Q.1Define relative velocity. Explain in detail the concept of relative velocity. Four particles A,B,C &D are
situated at the corners of a square ABCD of side ‘ a’ at t=0. Each of the particle moves with constant
speed v. A always has its velocity alon
g AB, B along BC, C along CD and D along DA. At what time will the
particles meet each other?

Q.2 What do you mean by a projectile? Show that the path of a projectile is always parabolic in nature.
For a projectile thrown at an angle ‘
Ɵ
’ with hprozontal a
nd velocity u, find:

i) Time of flight

ii) Horizontal range &

ii Maximum height attained.

Q3. (a)Derive the following Equations of motion for uniformly accelerated motion from velocity time
graph.

i)

v=u+ at ii) s = ut +1/2 at
2


iii) v
2
=u
2
+2as


(b)Also write equations for uniform motion.

Q 4(a)What is resolution of vectors. Explain the phenomena of pedaling of bicycle with the help of
resolution of vectors.


(b) Find the angle of projection for which horizontal range and max. height

are equal.

Q.5(a) Derive the position vector ‘



‘in three dimensions,



=


̂



̂



̂


with the help of vector addition.

(b) Find the resultant of two equal vectors if their resultant is equal to either of the two.


Topic:
-

Laws of Motion


Questions carrying 1 mark

1.

What is the unit of coefficient of friction?

2.

Name the factor on which coefficient of friction depends?

3.

What provides the centripetal force to a ca
r taking a turn on a level road?

4.

What is the direction of the acceleration of an object that is slowing down while heading northward?

5.

What is the acceleration of an object thrown straight up in the air, near the surface of the earth, at

the very t
op of its flight?

6.

What is the direction of the net force acting on an object that is moving in a circle with constant
speed?

7.

Is it possible to round a corner with constant velocity? Explain
.


8.

Automobile tyres

are generally provided with irregular projecti
ons over their surfaces. Why?

9.


Why the mud from moving wheels of vehicle fly off tangentially?

10.

A

body of mass m is moving on a horizontal table with constant velocity. What is the force on the
table?

1
1. Rocket works on which principle of conservation?

12. You can move a brick easily by pushing it with your foot on a smooth floor , but if you kick it then
your foot is hurt. Why?

13. W
hy does a swimmer push the water backwards?

14. A
ction and reaction ar
e equal in magnitude

and opposite in direction , then why do not they cancel
/balance each other?

15. Why do we pull the rope downwards for climbing up?

16. Mention a factor on which coefficient of friction depends.

17.

Carts with rubber tyres

are easier to pull than those with iron tyres. Why?

18.

Give a relation for impulse in scalar form.

19. It is easier to catch a table tennis ball, then a cricket ball, even when both are moving with same
velocity. Why?

20.

What is gravitational unit of
force?




Questions carrying 2 marks

21
.


Give the magnitude and direction of the net force acting on

(a) A drop of rain falling down with constant speed.

(b) A kite skillfully held stationary in the sky.


22
.

According to Newton' s Second Law, more massive objects tend to be harder to accelerate. Why
then do all objects, regardless of mass accelerate at the same rate when in free fall?

23
. Two blocks of masses m1, m2 are connected by light spring on a smooth ho
rizontal

surface. The two
masses are pulled apart and then released. Prove that the ratio of

their acceleration is inversely
proportional to their masses.


24
. A shell of mass 0.020kg is fired by a gun of mass 100kg. If the muzzle speed of the

shell is 80m
/s,
what is the recoil speed of the gun?


25
. Suppose that there is a first piece of rock which weighs 5 Newton. Force F is app
lied to this first piece
of rock

and it produces an acceleration of a. Now if there is a second piece of rock. What force need t
o
be applied to the second piece of rock to produce acceleration of 10a. Mass of both the pieces of rock is
same.



26
. Consider the problem on that on the object having initial mass of 4 kg. Two forces are acting on the
object. Force F
1

equal to 10 Newton and another force F
2

equal to 4 Newton. Direction of F
2

is opposite
to the direction of F
1
. Suppose that mass of the object decreases from 4 kg to 2 kg when forces are
applied to the object. Calculate the acceleration of the object.

27
.

Consider a person standing on a scale in an elevator. Will an accurate scale read more than, less

than, or equal to the weight of the person when the elevator is slowing down while moving downwards?

Explain
.

28
. Show that it is easier to pull a lawn roll
er than to push it.


29
. Explain t
he need of banking of tracks.

30
. Why frictional force gets increased when two surfaces in contact are p
olished beyond certain limit?

31
. Show that Newton’s first law of motion is contained in N
ewton’s second law of
motion.

32
. If action and reaction are always equal and opposite, explain how a cart drawn by
a horse moves
forward?

33.

Why is friction called self adjusting force?

34. Explain why is it difficult to move a cycle along a r
oad with its brakes on?

35. A thief jumps from the upper storey of house with a load on his back. What is the force of the load
on his back when the thief is in air ?

Questions carrying 3 marks

36
.

State Newton’s Second Law of Motion. Derive a mathematical formula to calculate fo
rce if mass
remains constant. Prove that it contains Newton’s first law.

37
.

State the law of conservation of momentum. Prove it by using second law of motion. Give two
situations where the linear momentum remains constant.

38
.

Two unequal masses m
1

and m
2

(m
2
>m
1
) are connected by a

string which passes over frictionless
pulley. Find the tension in the string and acceleration of masses.

39
.

A train runs along an unbanked circular bend of radius 30m at a speed of 54km/hr.

The mass of the
train is 106kg. What
provides the necessary centripetal force

required for this purpose,

t
he engine or
the rails? What is the angle of banking

required to prevent wearing out of the rail?


40
. Define coefficient of static friction and dynamic friction. Derive expression for th
e acceleration of the
body sliding on a horizontal plane having coefficient of friction µ
k
.


41
. What are concurrent forces? Prove that under the action of three concurrent forces F
1
,F
2
, and F
3
, a
body will be in equilibrium, when F
1
+F
2
+F
3
= 0.

42. Derive
a relation for the velocity at the lowest point and the hig
h
est point for looping the loop of

a
vertical circle
.

43. Prove that Newton’s second law is the real law of motion.

44.Define coefficient of friction angle of friction and hence derive a relation
between them.

45.



m1 T1 m2 T2 m3

Three blocks are connected as shown above and are on a horizontal frictionless table. They are pulled to
right with a force F=50 N . if m1= 5kg , m2=10kg and m3=
15kg, calculate tensions T1 and T2.

Questions carrying 5 marks


46
. (a) Define impulse. State its S.I. unit?

(b) State and prove impulse
-
momentum theorem?


47
.

Derive

an expression for the apparent weight of a person in a lift when (a) the lift is moving up with
acceleration (b) moving down with acceleration (c) moving up with acceleration (d) moving down with
deceleration (e) moving up or down with constant velocity.

48
. What is Banking of roads? Derive an expression for the maximum possible speed on a road of
banking angle Θ and
coefficient

of friction µ between the roads and the tyres.

49
.

(a) An objec
t is moving on a circular path in horizontal plane. Radius of path

is constant and speed is
v. Deduce expression for centripetal acceleration.

(b
)

Obtain an expression for the centripetal force required to make a body of mass m, moving with a
velocity v around a circular path of radius r.

50

(a).

Find an expression for velocity of recoil of gun.
(b)A hunter has a machine gun that can fire 50g
bullets with a velocity of 150ms
-
1
. A 60kg tiger springs at him with a velocity of 10 ms
-
1
. How many
bullets must the hunter fire into the target so as to sto
p him in his track?

51. (a). Define angle of friction and coefficient of friction.

(b). A bullet of mass 0.01kg is fired horizontally into a 4kg wooden block at rest on a horizontal surface.
The coefficient of kinetic friction between the
block and the su
rface is 0.25. T
he bullet remains
embedded in the bloc
k and the combination moves 20m

before coming to rest. With
wha
t speed did the
bullet strike the block?

MEASUREMENT AND WORK, ENERGY & POWER:

1 MARK QUESTIONS:

1.

Is work done a scalar or a vector?

2.

When is

work said to be 1 joule?

3.

What is the amount of work done by the earth’s Gravitational force in keeping the moon in a
circular orbit around the earth?

4.

Give two examples from daily life where according to physics work done is Zero?

5.

Force & displacement, bot
h are vectors. Yet their product work is a scalar quantity?

6.


Can acceleration be produced without doing any work? Give example.

7.

Under what condition is the work done by a force (a) Positive (b) Negative?

8.

Under what condition is the work done by a force Ma
ximum?

9.

Under what condition is the work done by a force Zero in spite of displacement being taking
place?

10.

What is the work done by the tension in the string of a simple pendulum?

11.

In a game of tug of war, what is the work done and by whom?

12.

A particle of
mass m has momentum P. What is its kinetic energy?

13.

If mechanical work is done on a body, will its K.E. increase or decrease?

14.

What is the source of K.E. of a falling rain drop?

15.

What is the source of K.E. of the blood coming out of the barrel of the rifle?

16.

W
ith what type of force is the potential energy associated?

17.

Define force constant. What is its SI unit?

18.

Can K.E. of a body be negative or positive?

19.

Define power and its SI unit?

20.

Calculate the power of a train in Watts which lifts a mass of 100 Kg to a heigh
t of 10 m in 20 s.

Two marks questions:

1.

Show that work may be expressed as scalar product of force and displacement.

2.

What is the work done by centripetal force? Explain?

3.

Calculate the work done by a car against gravity in moving along a straight highway. T
he mass of
the car is 400 Kg and the distance moved is 2 m.

4.

Show that the instantaneous power is given by dot product of force and velocity?

5.

A body is moved along a closed loop. Is the work done in moving the body necessarily Zero? If
not, state the condi
tions under which the work done over a closed path is always Zero?

6.

Find expression for Gravitational potential energy of mass m situated at a height h from the
surface of earth?

7.

Calculate the power of a motor which is capable of raising 2000 L of water in
5 min from a well
120 m deep.

8.

Two bodies of unequal masses have same linear momentum. Which one have greater K.E. and
why?

9.

Define atomic mass unit. Find its value?

10.

Express a light year in terms of astronomical unit.

11.

Give the correctness of relation v
2



u
2

= 2as by method of dimension.

12.

What are random errors? How is their effect eliminated?

13.

What do we mean by absolute error and relative error of a measurement?

14.

The radius of a solid sphere is measured to be 11.24 cm. What is the surface area of the sphere
to

appropriate significant figure?

15.

Find the Dimensional formula of (a) Gravitational Constant (b) Plank Constant

THREE MARK QUESTIONS:

1.

Describe the parallax method to measure the distance of a planet from the earth.

2.

Time period (T) of the simple pendulum may depend upon its mass m, length l and acceleration
due to gravity g . Find an expression for time period T by method of Dimension.

3.

A steel ball of radius r is allowed to fall under gravity through a viscous liquid
of coefficient of
viscosity

.

After some time the ball attains a constant velocity v. The terminal velocity depends
upon (a) weight of the ball mg (b) the coefficient of viscosity


(c) the radius of the ball r. By
method of dimension determine the relati
on expressing relative velocity.

4.

A small bucket containing water is rotating in a vertical circle. Obtain a expression for minimum
speed of bucket so that the water does not spill even at the highest point during its motion in a
vertical circle.

5.

By the met
hod of dimensions, find the value of acceleration of 8 m/s
2

in to km/hr
2
.

6.

Define elastic and inelastic collisions. A bullet is fired into a block of wood. It gets totally
embedded in it and the system moves together as one entity. State what happens to the

initial
kinetic energy and linear momentum of the bullet.

7.


Prove that in an elastic collision in one dimension, the relative velocity of approach before
impact is equal to the relative velocity of separation after impact.

8.

Prove that the total mechanical e
nergy of a freely falling body is always constant. Draw a graph
showing variation of P.E., K.E. and total energy.

9.

Show that the coefficient of restitution for one dimensional elastic collision is equal to 1.

10.

A bullet of mass 20 g is moving with speed of 15
0 m/s. It strikes a target and is brought to rest
after piercing 10 cm in to it. Calculate the average force of resistance offered by the target.

FIVE MARK QUESTIONS:

1.

State the principle of conservation of energy and show that this principle is valid in ca
se of a
freely falling body.

2.

What is two dimensional elastic collision? Discuss collision of two bodies in two dimensions.
Deduce from it the velocities of bodies in one dimension.

3.

What is the difference between work and energy?

An electric motor is used
to lift an elevator and its load (1500 kg) to a height of 20 m. the time
taken for the job is 20. The efficiency of the motor is 75%.

(a)

What is the work done

(b)

What is the rate at which the work is done?

(c)

At what rate is the energy supplied to the motor?

4.

(a)Two

blocks of wood A and B are coupled by a spring. They are placed on a frictionless table.
The spring is stretched and released. Show the following relation

K.E of A /K.E. of B =M
B

/ M
A

(b) A ball is dropped from rest from a height of 12 m. If it loses
25%

of K.E. on striking the
ground,

What is the height to which it bounces?


5. What do we mean by conservative and neoconservative forces? Explain the various properties
of conservative

force and show that gravitational force is a conservative force.

TOPIC: ROTATIONAL MOTION AND MOMENT OF INERTIA

SECTION: A (1 MARK)

1. Define angular momentum and give its SI unit.

2. State work energy theorem for rotational motion

3. Can a body in transl
atory motion have angular momentum?

4. Is it possible to open pen cap with one figure? Why?

5. Calculate angular velocity of ‘Hour Hand’ of clock.

6. Why is it easier to balance a bicycle in motion?

7. Why do you prefer to use a wrench with a long arm?

8.
What happens to duration of day night when tall buildings are constructed on the earth?

9. Why ships which have been emptied of Cargo are filled with the ballast?

10. A Rifle barrel has a spiral groove which imparts spin to the bullet. Why?

11. If one of
the particles is heavier than the other, to which will their centre of mass shift?

12. Can centre of mass of a body coincide with geometrical centre of the body?

13. Which physical quantity is represented by a product of the moment of inertia and the angu
lar
velocity?

14. What is the angle between





and





, if





and





denote the adjacent sides of a parallelogram drawn
from a point and the area of parallelogram is


AB.

15. Which component of linear momentum does not contribute to angular momentum?

16. A

disc of metal is melted and recast in the form of solid sphere. What will happen to the moment of
inertia about a vertical axis passing through the centre?

17. What is rotational analogue of mass of body?

18. What are factors on which moment of inertia de
pend upon?

19. Is radius of gyration of a body constant quantity?

20.

Is the angular momentum of a system always conserved? If no, under what condition is it
conserved?

SECTION: B (2 MARKS)

1.

A body projected into space explodes. What will be the nature of p
ath of its core?

2.

How does a diver manage to make somersaults in air?

3.

A disc of mass M and radius R is rotating with angular velocity ω. If gently, two masses ‘m’ are
placed at a distance R/2 on either side of the axis, what will be its angular velocity?

4.

Wh
at is the angular momentum with the projectile when it is at the highest point about an axis
through the point of projection?

5.

Can a body in translatory motion have angular momentum? Explain.

6.

Two circular discs A & B of the same mass and same thickness are
made of two different metals
whose densities are ‘d
A
’ and ‘d
B
’ (d
A
> d
B
). Their moments of inertia about the axis passing
through their centres of gravity and perpendicular to their planes are I
A

and I
B
. Which is greater
I
A

or I
B
?

7.

Two identical cylinders
‘run a race’ starting from rest at the top of inclined plane, one slides
without rolling and other rolls without slipping. Assuming that no mechanical energy is
dissipated in heat, which one will win?

8.

Briefly explain motion of Centre of Mass of Earth Moon
system.

9.

Name the physical quantity corresponding to inertia in rotational motion. How is it calculated?
Give its units.

10.

If earth were to shrink suddenly what would happen to the length of the day?

11.

Prove the Kepler’s law, that the line joining the sun and
the planet sweeps equal areas in equal
interval of time, using the angular momentum conservation with planet.

12.

Two eggs of same size and appearance but one is boiled and another is raw. How will you
recognized them without breaking them?

13.

The distance betwee
n the centres of carbon and oxygen atoms in Carbon Monoxide gas
molecules is 1.13Ȧ. Locate the centre of mass of the molecules relative to carbon atom.

14.

Write the rotational analogue of the following physical quantities (a) Force (b) Mass.

15.

What will be the

effect on the duration of the day if whole ice on the poles melts?

SECTION: C(3 MARKS)

1.

Calculate the power required by a force to turn a rigid body by some angle ‘
ɵ
’.

2.

How much fraction of the Kinetic Energy of rolling is purely (a) Translational (b) Rotat
ional?

3.

State and prove work energy theorem for rotational motion.

4.

If there are ‘n’ particles of masses m
1
, m
2
, ….m
n

distributed in space, write expressions for x, y
and z coordinates of Centre of Mass.

5.

Three particles each of mass ‘m’ are placed at three c
orners of an equilateral triangle of length
‘l’. Find the position of centre of mass in terms of coordinates.

6.

Find moment of inertia of a thin rod about an axis perpendicular to it and passing through its
mid
-
point.

7.

Establish a relation between angular mom
entum and moment of inertia of a rigid body. Define
moment of inertia in terms of it.

8.

Torques of equal magnitude is applied to a hollow cylinder and solid sphere, both having the
same mass and radius. The cylinder is free to rotate about its standard axis
of symmetry, and
the sphere is free to rotate about an axis passing through its centre. Which of the two will
acquire a greater angular speed after a given time?

9.

A tube of length ‘l’ is filled with a liquid of density ‘ρ’. Find the force experienced at one

of its
edge if rotated about the other edge with an angular velocity ω.

10.



A




ω
0




SECTION: D (5 MARKS QUESTION)

1.

Define Centre of Mass. State the need of determining Centre of Mass. Given a uniform circular
disc of mass M & radius R. A circular disc of radius R/2 is cut from it such that its circumference
t
ouches the centre of given disc. Find the position of centre of mass of the remaining disc.

2.

State the theorem of parallel & perpendicular axis of moment of Inertia. Moment of Inertia of a
uniform circular ring about an axis passing through its centre and p
erpendicular to the plane of
the ring is MR
2
, where M is the mass of the ring & R is its radius. Using these theorems
determine moment of Inertia of the ring about

(i) Any diameter of ring


(ii) Any tangent in the plane of the ring

(iii) Any tangent perpe
ndicular to the plane of ring.

3.

State the condition of equilibrium of a body. A body is constrained to rotate about Z
-
axis only.
State necessary conditions for the equilibrium of the body. Show that the torque required to
rotate the body is given by

τ
z

= xF
y

-

yF
x

4.

State Law of conservation of Angular momentum. A disc of Moment of Inertia I
1

is rotating
about an axis with angular velocity ω
1
, another disc of Moment of Inertia I
2

rotating with angular
velocity ω
2

in the same sense are brought in contact, find
the common angular velocity of the
system. Also find the loss in Kinetic Energy.

5.

What do you mean by the rolling motion? A body is rolling on an inclined surface without
slipping. Show that the relation for acceleration of the body is given by


. C

R/2 .



A disc rotating about its axis with angular speed ω
0

is
place lightly (without any translational push) on a
perfectly frictionless table. The radius of the disc is ‘R’.
What are t
he linear velocities of the points A, B and C
on the disc shown in figure? Will the disc roll in the
direction inclined?













Where symbols have their usual meanings.


A ring and a Disc of same mass & radius are allowed to roll on an inclined, out of the two which
one will reach the bottom first?

6.

Define angular velocity & angular acceleration. Also write their

SI units. Derive all three
equations for uniformly accelerated rotational motion i.e.


(i)

ω = ω
0

+ αt


(ii)

ɵ

= ω
0
t +


αt
2


(iii)

ω
2

= ω
0
2

+ 2α
ɵ


ω



V
cm

v
cm


O’

O’










a T
1

T
2

a



m
1



m
2



9. Define Torque and Angular momentum and establish relation between them. A flywheel of mass 500
Kg and diameter 1 m revolves about its axis. Its frequency of revolution is increased by 18 in

5 sec.
Calculate the torque required.

P

O

7. A body is rolling on a surface as shown in fig.
Taking O’ as centre of reference frame show that
kinetic energy of rolling motion is


K =


MV
cm
2

+


I
cm
ω
2

OR


K =


MV
cm
2
(






)

Where K is radius of gyration of the body



R

8. An inextensible string connecting two masses m
1

and m
2

is
passing over a disc shaped pulley of radius R and moment of
inertia I. For m
2
>m
1

find

(a) acceleration of the system

(b) Tensions in the strings T
1
& T
2

There is sufficient friction between string and pulley to have
its angular acceleration α = a/R


10. Define Moment of Inertia of rigid body. List out the factors on which it depends? Derive an
expression for (a) Kinetic Energy (b) Angular momentum (c) torque for a body having moment of inertia I
and angular veloc
ity ω rotating about fixed axis.

GRAVITATION

VERY SHORT ANSWER TYPE QUESTION

(OF ONE MARK)

1.

Name the weakest and the strongest force in nature?

2.

What is parking orbit?

3.

What is the value of gravitational potential at infinity?

4.

What is the value of escape velo
city from the surface of earth?

5.

What is the reason for absence of atmosphere in some planets?

6.

As a spacecraft moves from surface of earth to the moon, how does its weight vary?

7.

What is the value of gravitational field at a point inside a spherical shell?

8.

W
hat is the basis for the second law of Kepler?

9.

What does spring balance measure: mass or weight?

10.

What is the value of orbital velocity for a satellite

orbiting close to the surface of earth?

11.

If the earth stops rotating about its own axis, what is the effec
t on the value of g on the surface
of earth?

12.

What is the value of time period of a geostationary satellite?

13.

What will be the value of time period of a simple pendulum in an artificial satellite?

14.

If the polar ice caps on the earth melt,

how will the length

of the day be affected?

15.

Two artificial satellite,

one close to the surface and other away are revolving around the earth,

which has larger speed?

16.

How does the orbital velocity of a satellite depends on the mass of the satellite?

17.

What is

the condition for a uniform spherical mass to be a black hole?

18.

Name the satellite used for TV and Radio broadcast?

19.

Which is greater
-
the attraction of earth for 1kg mass or attraction of 1kg mass for earth?

20.

Why do you feel giddy while moving on a merry
-
go
-
round?


SHORT ANSWER TYPE QUESTION

(OF TWO MARKS)

1.

A body weighs 63N on the surface of earth.

What is the gravitational force on it due to the
earth at a height equal to half the radius of earth?

2.

Assuming the earth to be a sphere of uniform mass den
sity ,how much would a body weigh
half way down to the centre of the earth if it weighed 250N on the surface?

3.

What is geostationary satellite
?
What are the condition for a satellite to become the
geostationary satellite?

4.

The radii of two planets are
R and 2R respectively and their densities d and d/2 respectively.

What is the ratio of acceleration due to gravity at their surface?

5.Why is the weight of a body at the poles more than the weight at the equator?

Explain.

6.What is the maximum value of pot
ential energy that can a heavenly body?

Give the general
expression for potential energy of an object near the surface of earth.

7.What happens to a body when it is projected vertically upwards from the surface of earth with
a speed of 11200m/s,andwhy?

Com
pare escape speeds for two planets of masses M and 4Mand
radii 2R and R respectively?

8.The time period of the satellite of the earth is 5hours.If the separation between the earth and
satellite is increased to 4 times the previous value,

than what will be
the new time period of the satellite?

9.

Mention the conditions under which the weight of a person can become zero?

10.

What would happen if the force of gravity were to disappear suddenly?

11.

What is acceleration due to gravity?

Establish relation
between g and G?

12. State two point of difference and similarity between the gravitational force and electrostatic
force?

13. What is gravitation?

State universal law of

Gravitation?

14.The distances of two planets from the sun

are 10
12

and 10
10

meters re
spectively. What is the
ratio of periods of these two planets?

15.What do you mean by Intensity or strength of gravitational field ?Is it a vector or scalar
quantity.give its unit and dimensions.


SHORT ANSWER TYPE QUESTION(OF THREE MARKS)

1. State and exp
lain the Kepler’s laws of planetary motion. Name the physical quantities which remain
constant during the planetary motion?

2. Find the potential energy of a system of four particles placed at the vertices of a square of side l.

Also
obtain the potential
at the centre of the square?

3.

A 400kg satellite is in the circular orbit of radius 2R
E

about the earth.

How much energy is required to
transfer it to a circular orbit of radius 4R
E
?

What are the changes in the kinetic and potential energy?

4. Find the pe
rcentage decrease in the weight of a body when it is taken 16km below the surface of
earth.

Take radius of earth as 6400km.

5. Find the height from the

surface of earth at which weight of a body of mass m will be reduced by
36%of its weight on the surface.

Take radius of earth as 6400km.

6.

What do you mean by intensity or strength of gravitational field? Prove that the intensity of
gravitational field of earth at any point is equal to acceleration due to gravity at that point.

7. What do you mean by accele
ration due to gravity?

Establish relation between g and G.

8.

Find the expression of total energy of a satellite revolving around the surface of earth.

What is the
significance of negative sign in the
expression?

9.

What are geostationary satellites?

Calc
ulate the height of the orbit of a geostationary satellite.

10.
Calculate the escape speed for an atmospheric particle 1600 km above the earth’s surface, given
that the radius of the earth is 6400 km and acceleration due to gravity on the surface of earth
is 9.8 ms
-
2
.

LONG ANSWER TYPE QUESTION

(OF FIVE MARKS)

1.

Define escape velocity.

Derive an expression for the escape velocity of an object from the surface of
the earth.

Does it depend on the location from where the object is projected?

2.

What do you
mean by acceleration due to gravity?

Discuss its variation with depth and height.

3.

What do you mean by gravitational potential energy of a body?

Derive an expression for the
gravitational potential energy of a body of mass m

located at a distance r from
centre of the earth?

4.

Define orbital velocity and time period of a

Satellite.

Derive an expression for

orbital velocity and time
period of a Satellite orbiting very close to the surface of Earth and hence find the ratio of the orbital
velocity and escape

velocity?

5.

State

Kepler’s laws of planetary motion and hence deduce Newton’s law of gravitation from Kepler’s
law of periods.


PROPERTIES OF BULK MATTER

1 Marks Questions

Q1. Why are springs made of steel and not of copper?

Q2.Young’s modulus of wire o
f length L and radius r is Y. If the length is reduced to L/2 and radius to r/4,
what will be its Young’s modulus?

Q3. Which is more elastic water or air?

Q4.What is the value of modulus of rigidity for an incompressible liquid?

Q5. Why are electric poles
given hollow structure?

Q6. What is the value of surface tension at critical temperature?

Q7.Why is it difficult to stop bleeding from a cut in human body at high altitudes?

Q8. Mention two applications of Stoke’s law.

Q9. Fog particles appear suspended in the atmosphere , give reason.

Q10. A small sphere is dropped from rest into a viscous liquid. Draw its velocity time graph, also indicate
the terminal velocity on the graph.

Q11. Write down the following liquids in inc
reasing order of surface tension:

a)

Water



b)
Mercury

c )
Soap solution

Q12. Why do air bubbles move in upward direction?

Q13. Explain why the blood pressure in humans is greater at the feet than at the
brain?

Q14. What is the range for
Reynolds

number for the streamline motion of liquid?

Q15. Why do the boat moving parallel to each other attract each other?

Q16. Why two streamlines cannot cross each other?

Q17. Which fundamental
laws form

the basis of eq
uation of continuity?

Q18. State the principle involved in the flight of
aero plane
.

Q19. Why is it easier to swim in sea water than in river water?

Q20. What is value of Young’s modulus for a perfect rigid body?

2 Marks Questions

Q1 state and prove equati
on of continuity.

Q2 On the basis of stress
-
strain curve
differentiate between

ductile and brittle material.

Q3 Explain
Magnus

effect with the help of diagram.

Q4 What do you mean by compressibility. Why are solids least compressible and gases most .

Q5 D
istinguish between stream line flow and turbulent flow of liquid

Q6 At what speed will the velocity head of steam of water be equal to 40cm

Q7 Can Bernoulli’s equation be used to describe the rapid flow of water through a river ? Explain.

Q8 why does an o
bject entering the earth’s atmosphere at high speed catch fire.

Q9 Define angle of contact of a liquid with a solid surface on what factors does it depend.

Q10 A square plate of 0.10m side moves parallel to another plate with a relative velocity of 0. 10
m/s
both the plates being immersed in water, if the viscous force is 2×10
-
3
N and coefficient of viscosity of
water is 1×10
-
3
Pascal

sec. What is the separation between the two plates?

Q11. The spherical raindrops of equal size are falling vertically thro
ugh air with a terminal velocity of o.1
m/s. what would be the terminal velocity if the drops were to coalesce to form a single large drop?

Q12. Define surface tension mathematically. What is its S. I. unit? Write its dimensional formula.

Q13. What is the
total potential energy of a soap film formed on a frame of area 6×10
-
4
m
2
, given
surface tension of soap solution is 0.028N/m.

Q14. Water is depressed in a glass tube bore coated with paraffin wax. why?

Q15. A large soap bubble is formed at one end of a n
arrow bore tube and a small one at the other end.
Which one will grow at the expense of the other. Give reason too.

3 Marks Questions

Q1 State Pascal’s law . Using this law explain the working of hydraulic brakes

Q2 State and prove stokes law.

Q3 Define t
erminal velocity and derive its expression

Q4


What is the pressure inside the drop of mercury of radius 3mm at room temperature surface tension
of mercury at that temperature is 4.65x10
-
1
N/m atmosphere pressure 1.01x 10
5
pa. Also give the excess
pressure

inside the drop.

Q5 (i) What is the largest average velocity of blood flow in an artery of radius 2x10
-
3

m .if the flow must
remain laminar?

(ii)What is the corresponding flow rate? (take η= 2.08x10
-
3
Pa
-
s)

Q6 Explain the following

(1)

Concrete beam used in la
rge buildings have greater depth than breadth

(2)

Load bearing bars are generally made in I sections.

(3)

Pillar with distrusted ends is preferred over a pillar with rounded ends.

Q7 (i)
explain

the role of detergent in washing of clothes


(ii) Hydrostatic p
ressure is a scalar quantity even though pressure is force/area


(iii) A drop of liquid under no external forces is always spherical

Q8 A plane is in level flight at constant speed and each of its two wings has an area of 25m
2

if the speed
of air is 1
80km/h over the lower wing surface determine the plane’s mass take air density to be 1kg/m
3

and g=9.8m/s
2
.

Q9Write the Bernoulli theorem in terms of pressure head, gravitational head and velocity head . What
will be the expression for horizontal flow of li
quid during a certain windstorm light roof may be blown
off?

Q10 (1) What is the effect of temperature on

(a) Viscosity of liquid

(b) Surface tension of a liquid

(c)viscosity of gases

(2)

which is more viscous honey or water and why?

5 Marks Quest
ions


1.(a) State and prove Bernoulli’s theorem.


(b) Write any two limitations and applications of this theorem.

Q2. (a) What is meant by capillarity?


(b) Derive ascent formula.


© Why does liquid not flow through a tube of insufficient length?

Q3. (a)
Derive an expression for the excess pressure in a soap bubble.


(b) Explain what determines the shape of a a liquid meniscus in a narrow tube.

Q4. Discuss stress/ strain graph for a loaded steel wire and hence explain the following terms:

(a)

Elastic limit


(b)Yield point


( c)Permanent set (d)Tensile strength

Q5. (a) Name a device used to measure the rate of flow of a liquid through a pipe.


(b) State the principle on which it works.


( c) Describe its construction and working.

Q6. (a) Esta
blish the relation between surface tension and surface energy.

(b) Two wires of diameter
0.25 cm one made of steel and the other made of brass are loaded as shown in the
figure. The

unloaded
length of steel wire is 1.5 m and that of brass is 1.0 m. Comput
e the elongation of the steel and the brass
wire.





1.5 m(steel)






4.0 kg



1.0

m(brass)


6.0 kg




1. Thermal properties of matter


2. Thermodynamics


3. Kinetic theory of gases

Section A

Each question carry one mark.

1. Given Samples of 1 cm3 of Hydrogen and 1 cm3 of oxygen, both at N. T. P. which

sample
has a larger
number of molecules?

2. State the law of equi
-
partition of energy?

3. On what factors, does the average kinetic energy of gas molecules depend?

4. What is the relation between pressure and kinetic energy of gas?

5. Why is mercury used in ma
king thermometers?

6. Show the variation of specific heat at constant pressure with temperature?

7. Two thermometers are constructed in the same way except that one has a

spherical bulb and the
other an elongated cylindrical bulb. Which one will

response

quickly to temperature change?

8. Define triple point of water?

9. Why the clock pendulums are made of invar, a material of low value of

coefficient of linear
expansion?

10. Why is temperature gradient required for flow of heat from one body to another?

11. If a body has infinite heat capacity? What does it signify?

12. Why is latent heat of vaporization of a material greater than that of latent heat of

fusion?

13. Draw a P


V diagram for Liquid and gas at various temperatures showing critical

point?

1
4. On a winter night, you feel warmer when clouds cover the sky than when sky is

clear. Why?

15. If a body is heated from 270 C to 9270C then what will be the ratio of energies of

radiation emitted?

16. If the temperature of the sun is doubled, the rate of

energy received on each will

increases by what
factor?

17. Can you design heat energy of 100% efficiency?

18. Draw a p


v diagram for isothermal and adiabatic expansion?

19. State zeroth law of thermodynamics?

20. Differentiate between isothermal and
adiabatic process?


Section B

Each question carry two marks.

1. The earth without its atmosphere would be inhospitably cold. Explain Why?

2. Calculate the degree of freedom for monatomic, diatomic and

triatomic gas?

3. A thermometer has wrong
calibration. It reads the melting point of ice as


100C.

It reads 600C in
place of 500C. What is the temperature of boiling point of water

on the scale?

4. If the volume of block of metal changes by 0.12% when it is heated through 200C.

What is the co
-
eff
icient of linear expansion of the metal?

5. A ball is dropped on a floor from a height of 2cm. After the collision, it rises up

to a height of 1.5m.
Assuming that 40% of mechanical energy lost goes to

thermal energy into the ball. Calculate the rise in
te
mperature of the ball in thecollision. Specific heat capacity of the ball is 800J/k. Take g = 10m/s2

6. A 0.20 Kg aluminum block at 800C is dropped in a copper calorimeter of mass

0.05 Kg containing 200
cm3 of ethyl alcohol at 200C. What is the final

tempe
rature of the mixture? Given Density of ethyl
alcohol = 0.81 g | cm3 ;

specific heat of ethyl alcohol = 0.6 cal | g | 0C ; specific heat of copper = 0.094
cal |g | 0C, specific heat of Al = 0.22 cal | g | 0C?

7. Show that CP
-

CV = R Where [CP = specific h
eat at constant pressure; CV = specific

heat at constant
volume and R = Universal Gas constant] for an ideal gas?

8. From what height should a piece of ice fall so that it completely melts? Only one


quarter of heat
produced is absorbed by the ice. Given
latent heat of ice is 3.4 × 105

J | Kg and acceleration due to
gravity, g = 10m | s2?

9. Two rods A and B are of equal length. Each rod has its ends at temperatures T1

and T2. What is the
condition that will ensure equal rates of flow of heat through

the r
ods A and B?

10. Animals in the forest find shelter from col
d in holes in the snow. Why?

11. The tile floor feels colder than the wooden floor even though both floor materials

are at same
temperature. Why?

12. A Carnot engine absorb 6×105 cal at 2270c cal
culate work done per cycle by

the engine if it sink is at
1270c?

13.A refrigerator placed in a room at 300 K has inside temperature 264K. How

many calories of heat
shall be delivered to the room for each 1 K cal of energy

consumed by the refrigerator, idea
lly?

14. If the door of a refrigerator is kept open in a room, will it make the room warm

or cool? Why?

15. State first law of thermodynamics and apply this law to isochoric and isobaric process.


Section C
Each question
carries

three marks.

1. If half mol
e of helium is contained in a container at S. T. P. How much heat energy

is needed to double
the pressure of the gas, keeping the volume of the gas

constant? Given specific heat of gas = 3J | g |K.

2. Five moles of an ideal gas are taken in a Carnot engine

working between 1000C

and 300C. The useful
work done in 1 cycle is 420J. Calculate the ratio of the

volume of the gas at the end and beginning of the
isothermal expansion?

3. Calculate difference in efficiency of a Carnot energy working between:
-

1) 400
K and 350K

2) 350K
and 300K
.

4.

One kilogram molecule of a gas at 400k expands isothermally until its volume is

doubled. Find the
amount of work done and heat produced?

5.

How do you derive Newton’s law of cooling from Stefan’s law?

6.

Define the terms

reflectance, absorptance and transmittance. How are they

related?

7.

Differentiate between conduct
ion, convection and radiation?

8
. What is Mean free path? Derive an expression for it.

9.

Derive an expression for work done during isothermal process.

Section D

Each question carry five marks.

1.(a) What are the basic assumptions of kinetic theory of gases? On their basis derive an expression for
the pressure exerted by an ideal gas.

.(b)At what temp is r.m.s of an atom in an argon gas cylinder is equal
to the rms speed of helium gas
atom at
-
20
o
C.Atomic mass of argon =39.9u and that of helium =4u. Hint v=(3RT/M)
1/2

2. (a) Prove that
ɑ=β/2=γ/3.Where the symbols have their usual meanings in thermal expansion.
(b)Brass wire 1.8m long at 27
0
C is held taut
with little tension between two rigid supports. If the wire is
cooled to a temperature of
-
39
0
C, what is the tension developed in the wire, if its diameter is 2.0mm?
Coefficient of linear expansion of brass is 2.0 X10
-
50
C
-
1
,Youngs

modulus of brass 0.91 X 10
11
Pa.

Hint
∆l=lα(T
2
-
T
1
),stress=strain x youngs modulus.

3.

(a)What is Carnot engine? Derive an expression for efficiency of Carnot engine.


(b) A steam engine delivers 5.4 X 10
8
J of work and services 3.6 X 10
9
J of heat from i
ts boiler. What is
efficiency of the engine? How much heat is wasted to the sink?

4.

(a). Discuss briefly energy distribution of a black body radiation. Hence deduce

Wien’s

displacement
law?

(b)The spectral energy distribution of the sun has maximum at 475
3A
0
.If the temp of sun 6050K.What is
temp of star for which this maximum is at 9506A
0
?


Hint λ
m
=b/T.

5.

(a)On what factors does the rate of heat conduction in a metallic rod in the steady state depend?
Write the necessary expression and hence define the co
efficient of thermal conductivity. Write its SI
unit.

(b). A room has a 4m x 4m x10cm concrete roof (K1 = 1.26w|m|0C). At some instant,

the temperature
outside is 46
0
C and inside is 32
0
C.


(
1) Calculate amount of heat flowing per second into the room thr
ough the roof.


(
2) If bricks (K2


0.56w |m|0c) of thickness 7.5cm are laid down on roof, calculate

the new rate of
heat flow under the same temperature conditions?


Waves and Oscillations

(1 marks questions)

1. Which of the following relationships betw
een the acceleration ‘a’ and the displacement ‘x’ of a
particle involve simple harmonic motion?

(a) a=0.7x (b) a=
-
200x
2

(c) a =
-
10x (d) a=100x
3

2.

Can a motion be periodic and not simple harmonic? If your answer is yes,
give an example and if
not, explain why?

3.

A girl is swinging in the sitting position. How will the period of the swing change if she stands up?

4.

The maximum velocity of a particle, executing S.H.M with amplitude of 7mm is 4.4 m/s. What is
the period of
oscillation?

5.

Why the longitudinal wave are also called pressure waves?

6.

How does the frequency of a tuning fork change, when the temperature is increased?

7.

An organ pipe emits a fundamental node of a frequency 128Hz. On blowing into it more strongly
it produ
ces the first overtone of the frequency 384Hz. What is the type of pipe

Closed or Open?

8.

All harmonic are overtones but all overtones are not harmonic. How?

9.

What is the factor on which pitch of a sound depends?

10.

Write the Newton’s formula of velocity of sou
nd in air.

11.

Write the necessary correction in Newton’s formula for speed of sound in air by Laplace?

12.

Is speed of sound in air depends on pressure? Justify your answer?

13.

Give expression for beat frequency?

14.

State Doppler’s effect?

15.

Why stationary waves are call
ed standing waves?

16.

Write the expression for fundamental frequency in an organ pipe open at one end?

17.

Write the expression of displacement in plane progressive wave?

18.

What is the phase difference between incident and reflected wave from the rigid and open
bou
ndary?

19.

Mention two applications of dopller’s effect?

20.

What effect on the time period of simple pendulum when it taken to the moon ?


(2 Marks questions)

1.

At what points is the energy entirely kinetic and potential in S.H.M? What is the total distance
travell
ed by a body executing S.H.M in a time equal to its time period, if its amplitude is A?

2.

A simple pendulum consisting of an inextensible length ‘l’ and mass ‘m’ is oscillating in a stationary
lift. The lift then accelerates upwards with a constant accelerat
ion of 4.5 m/s
2
. Write expression for
the time period of simple pendulum in two cases. Does the time period increase, decrease or remain
the same, when lift is accelerated upwards?

3.

Does the function y = sin
2
ωt represent a periodic or a S.H.M? What is perio
d of motion?

4.

All trigonometric functions are periodic, but only sine or cosine functions are used to define SHM.
Why?

5.

A simple Harmonic Motion is represented by







x = 0
. What is its time period?

6.

The Length of a simple pendulum executing SHM is
increased by 2.1%. What is the percentage
increase in the time period of the pendulum of increased length?

7.

A simple Harmonic motion has an amplitude A and time period T. What is the time taken to travel
from x = A to x = A/2.

8.

An open organ pipe produces a
note of frequency 5/2 Hz at 15
0
C, calculate the length of pipe.
Velocity of sound at 0
0
C is 335 m/s.

9.
An incident wave is represented by Y(x, t)=20sin(2x
-
4t).Write the expression for reflected wave


(i) From a rigid boundary


(ii) From an o
pen boundary.


10.

Explain why


(i) in a sound wave a displacement node is a pressure antinode and vice
-

versa


(ii) The shape of pulse gets
-

distorted during propagation in a dispersive

medium.

11. Derive an expression for apparent freque
ncy when a source of sound approaches stationary observer
with velocity Vs.

12. Derive Laplace correction in Newton’s formula in velocity of sound.

13. prove that beat frequency is the difference of individual frequency of components waves.

14. Give two di
fferences between damped & undamped oscillations.

15. Explain the motion of simple pendulum is S.H.M.

(3

Marks Questions)

1.

The speed of longitudinal wave `V` in a given medium of density ρ is given by the formula, use this
formula to explain why the speed o
f sound in air.



(a) is independent at pressure








(b) increases with temperature and








(c) increases with humidity


2.

Write any three characteristics of stationary waves.

3.

Show that the speed of sound in air increased by .61m/s for every 1
0

C rise of temperature.

4.

Find the ratio of velocity of sound in hydrogen gas γ
5
7


to that in helium gas

γ
3
5


at the same temperature. Given that molecular weight of hydrogen and helium are 2 and 4
respectively.

5.

The equation of a plane progressive wave is,














where y & x are in cm & t in
second. Calculate the amplitude, frequency, wavelength & velocity of the wave.


6.

Write displacement equation respecting the following condition obtained in SHM
.


Amplitude = 0.01m


Frequency = 600Hz


Initial phase =



7.

The amplitude of oscillations of two similar pendulums similar in all respect are 2cm & 5cm
respectively. Find the ratio of their energies of oscillations.

Ans.














(


)






8.


What is the condition to be satisfied by a mathematical relation between time and displacement to
describe a periodic motion?

9.
A spring of force constant 1200N/m is mounted horizontal table. A mass of 3Kg is attached to the
free end of the spring, pulle
d sideways to a distance of 2.0cm and released.


(i) What is the frequency of oscillation of the mass?


(ii) What is the maximum acceleration of the mass?


(iii) What is the maximum speed of the mass?


10.

Which of the following function of time represent, (a) simple harmonic (b) periodic but not SHM and
(c) non periodic ?


(i) Sin

t
-

Cos

t (ii)




(iii)









(iv)











(5 Marks Questions)

1.

(a) A light wave is reflected from a mirror. The incident & reflected wave superimpose to form
stationary waves. But no nodes & antinodes are seen, why?


(b) A standing wave is represented by y=2ASinKxCoswt.If one of the component wave is











what is the equation of the second component wave?

2.
Discuss Newton’s formula for velocity of sound in air. What correction was made to it by Laplace and
why?

3.

(a) What are beats? Prove that the number of beats per second is equal to the
difference between
the frequencies of the two superimposing wave.


(b) Draw fundamental nodes of vibration of stationary wave in (i) closed pipe, (ii) in an open pipe.

4.
Discuss the formation of harmonics in a stretched string. Show that in case of
a stretched string the
first four harmonics are in the ratio 1:2:3:4.

5.

Explain Doppler’s effect of sound. Derive an expression for the apparent frequency where the source
and observer are moving in the same direction with velocity Vs and Vo respectively,

with source
following the observer.

6.
For a travelling harmonic wave,


















where x & y are in cm and t in
second. What is the phase difference between oscillatory motions at two points separated by a distance
of (i) 4cm (ii) 0.5m

(iii)










?

7.


(i)
A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal
vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?

(ii)
A pipe 20 cm long is closed at one end. Which har
monic mode of the pipe is resonantly exited
by a 430 Hz source? Will this same source be in resonance with the pipe if both ends are open?
(Speed of sound = 340 m/s).

8.

A train stands at a platform blowing a whistle of frequency 400 Hz in still air.

(i
)
What is the frequency of the whistle heard by a man running


(a)Towards the engine 10 m/s.


(b) Away from the engine at 10 m/s?

(ii)
What is the speed of sound in each case?

(iii)
What is the wavelength of sound received by the running man in
each case?

Take speed of sound in still air = 340 m/s.

9.

What is a spring factor? Derive the expression for resultant spring constant when two springs having
constants k
1
and k
2
are connected in (i) parallel and (ii) in series.

10.

Show that for a particle in
linear S.H.M., the average kinetic energy over a period of oscillation is
equal to the average potential energy over the same period. At what distance from the mean
position is the kinetic energy in simple harmonic oscillator equal potential energy?

VALUE

BASED QUESTIONS

1.

Kanha visited his village during the holidays.

One

day he went for a morning walk.

He saw a person
trying to push a
cart, but was

not in a position to do so because of the muddy field.

Kanha asked him for
his help.

He spread some pieces of stones along with the
person, below

the wheel cart.

The wheel of the
cart came out of the mud with his effort.

(i) What values were shown by
Kanha?

(ii) What techniques were used by
Kanha?

(iii) Name one advantage and one disadvant
age of the physical quantity involved in second question in
our day to day life.

2. One day Ram visited a nearby book shop along with his father to purchase some fiction.

His father
opened the book and started to read the preface of the book,

in the
meanwhile Ram observed that his
father was unable to read the book properly.

He requested his father to visit the nearby eye

clinic and
get checked his eyesight

.Next day Ram along with his father visited the eye

clinic,

where doctor advised
him to put on

the spectacles of power 2.5D.

(i) What values were executed by
Ram?

(ii) From what defect the father of Ram was suffering.

(iii)Find the focal length and nature of the
lens

used.

3. Mr. David started ice skating recently under the guidance of Mr. Franklin
.

On the very first day Mr.
David h
eld

the dumbles in his hands and started spinning on an ice track.

Suddenly

he fell down and got
injured,

Mr.

Franklin

quickly rushed toward him and carried him to a nearby hospital for the further
treatment.

(i)What valu
es were shown by Mr.

Franklin.

(ii) Why Mr. David fell down.

(iii) Name the principle behind the spinning of an ice
skater
.

4.

Pinki along with grand father went to a nearby park for morning walk on a Sunday morning. There she
saw a swing and requested her grandfather to swing herself. Her grandfather was pushing the swing and
after some time he got tired and set down in the nearb
y bench. Pinki stands in the running swing due to
which the speed and hence
the amplitude

of vibration of the swing increased by large amount,

and

Pinki
started crying.

After seeing
this
, a

boy walking there rushed toward the swing and advised her to sit
down in the swing.

Now the swing started to swing with the lower speed and seeing this Pinki

stopped

crying.

(i) What were the values displayed by the boy.

(ii) What is the cause of the change in the speed of the swing?

(iii)Why the pendulum clock got slow
ed down on the mountain.

5.

Three friends went to a hill station to celebrate the eve of New Year.

The younger was making a
phone call and get separated from his friends.

He shouted loudly naming his friends .He observed that
somebody was copying him and s
houting the same words.

He started crying,

and got depressed and
terrified.

After some time his friends reached there ,

seeing his condition they sprinkled some water on
his face and asked him about the mis

happening

occurred.

His friend told him that the

sound
heard

by
him was nothing but an echo.

(i) What values were shown by his friends?

(ii) What do you mean by an echo?


(iii) How the echo is formed.

6.

An old woman crossing the road was holding a money purse. She was not able to walk .A pick
pocket snatc
hes away her purse. A school student of class X having seen this incident tries to
help that old lady. He informs the police Inspector who stands nearby. The Inspector collects the
money purse from the pickpocket and hand it over to the old lady. (a)What v
alues do you find in
the school student? (b)Also the police inspector in a jeep is chasing the pickpocket on a straight
road. The jeep is going at its maximum speed ‘v’. The pickpocket rides on the motorcycle of a
waiting friend when the jeep is at a dista
nce ‘
d
’ away. and the motorcycle starts with a constant
acceleration ‘a’. Show that the pickpocket will be caught if v≥√2ad.

7.


Sita a student of class XII was suffering from malaria. The area is full of mosquitoes. She was not
having mosquito net. Her frien
d Geeta has an extra net. She gave it to Sita. Also she took Gita to
a Doctor, got her medicines. After a week Sita became normal (a) Comment upon the qualities
of Sita. (b) The mosquito net over a 7 m X 4mbed is 3m high. The net has a hole at one corner o
f
the bed through which a mosquito enters the net. It flies and sits at the diagonally opposite
upper corner of the net(i) Find the magnitude of the displacement of the mosquito (ii)Taking the
hole as the origin, the length of the bed as the X
-
axis, its wi
dth as the Y
-
axis and vertically up as
the Z
-
axis, with the components of the displacement vector.

8.


Krishna went for sightseeing to a nearby river along with his physics teacher. He noticed
that the wind was blowing from the side and the sailboat still con
tinued to move forward.
He was surprised. He asked his physics teacher the explanation of this situation. The teacher
having noticed his interest explained the concept through a small example. The physics of
sailing is very interesting in that sailboats do

not need the wind to push from behind in
order to move. The wind can blow from the side and the sailboat can still move forward.
The answer lies in the well
-
known principle of aerodynamic lift. Imagine you are a passenger
in a car as it's moving along, an
d you place your right hand out the window. If you tilt your
hand in the clockwise sense your hand will be pushed backwards and up. This is due to the
force of the air which has a sideways component and upwards component (therefore your
hand is pushed back
wards and up). (a) What values could you find in Krishna?
(b)
Also
explain what Magnus effect is.

9.

Having found his mother suffering from fever
Venkat took
her to the doctor for treatment.
While checking the status, the doctor used a thermometer to know the

temperature of the
body. He kept the thermometer in the mouth of the patient and noted the reading as 102


F.
Doctor gave the necessary medicines. After coming home, Venkat asked his mother, who is a
science teacher , why mercury is used in a thermometer
when there are so many liquids. Then
his mother explained the reason. (a) Comment upon the values of the mother. (b)A newly
designed thermometer has its lower fixed point and upper fixed point marked at 5◦and 95◦
respectively. Compute the temperature on th
is scale corresponding to 50◦C

10.

Having seen a big stone falling from the top of a tower Ravi pulled his friend Kiran away. The
stone hit Ravi slightly and he got hurt. But he was saved from a major accident. (a)What made
Ravi act in such a way. (b)From the
top of a tower 100 m in height, a ball is dropped and at the
same time another ball is projected vertically upwards from the ground with a velocity of 25
m/s. Find when and where the two balls meet. Take g = 9.8 m/sec2.