Introduction
In this chapter we shall study about gravitation and universal law of gravitation. We will discuss about the motion of the body under the influence of gravitation. How the weight of the body varies from one place to another? It was Sir Isaac Newton who first gave the term gravitation when he saw an apple falling from a tree and thought that 'why an apple fall towards the earth and not going otherwise'. Later he realized that it is because earth attracts every object towards itself with a force called the gravitational force. Later on the generalized the idea and said that not only the earth, but every other object in this universe attract each other with a force. Our knowledge about gravitation did not develop only as a result of Newton's observation of a falling apple. Before Newton there were many scholars who had been using the term Gurutva akarshan in India. Before Newton many scientist such as Aryabhatta and Kepler studied about the motion of the planet. It was Kepler who described 'how the planet moves around the sun?'.
Newton's laws of motion helps us to understand about the force which cause a planet's motion.. 
Power
The rate of doing work is called power.
\[(P)=\frac{\text{work}\,\text{done}\,\text{(W)}}{\text{time}\,\text{taken}\,\text{(t)}}=\,\,\text{or}\,\,P=\frac{W}{t}\]
Commercial Unit of Energy
The unit joule is too small and hence is inconvenient to express large quantities of energy. So, we use a bigger unit of energy called kilowatt hour (kW h).
1 kW h = 1 kW \[\times \] 1 h
= 1000 W \[\times \] 3600 s
= 3600000 J
1 kW = 3.6 \[\times \] 106 J
Which one of the following is the commercial unit of energy?
(a) Joules
(b) Watt
(c) KW
(d) KWh
(e) None of these
Answer: (d)
One kilowatt hour is equal to:
(a) \[36\times {{10}^{6\,}}J\]
(b) \[136\times {{10}^{6}}J\]
(c) \[3.6\times {{10}^{6}}J\]
(d) \[1.36\times {{10}^{6}}J\]
(e) None of these
Answer: (c)
One horse power is equal to:
(a) 746 watt
(b) 74.6 watt
(c) 7.46 watt
(d) 746 kw
(e) None of these
Answer: (a)
Work done by a string when a stone is tied to it and whriled in a circle is:
(a) Positive
(b) Negative
(c) Zero
(d) All of these
(e) None of these
Answer: (c)
Transformation of energy
The change of one form of energy into another is called transformation of energy. When a body falls from a certain height, its potential energy changes into kinetic energy.
Wind Energy \[\to \] Electricity \[\to \] Light + Heat
(1) A stone when is released from a height, the potential energy of the stone is gradually changed into kinetic energy and reverse happens when the stone is thrown upward.
On the other hand, when a body is thrown up, its kinetic energy gradually changes into potential energy.
(2) At a hydroelectric power house, the potential energy of water is transformed into kinetic energy and then into electrical energy.
(3) At a thermal power station, the chemical energy of coal is converted into heat energy which is further converted into electrical energy.
(4) Heat energy is converted into kinetic energy by the steam engine.
The Law of Conservation of Energy
According to the law of conservation of energy. Energy can neither be created nor destroyed, only it can be transformed from one form to another. But the total energy of the entire system always remains constant.. 
Energy
The word energy is used daily in our daily life. In science we give the word a definite and specific meaning. The energy is defined as the ability to do the work. Thus, the unit of energy is same as that of work. That is the unit of energy is joule. 1 joule is the energy required to do the work of 1 joule. The larger unit of energy is kilojoule.
1 kj = 1000 joule
The object which possess energy can exert a force on another object. When this happens, the energy is transferred from the former to the latter. The second object may move as it receives energy and therefore do some work. There are different forms of energy. The different forms of energy includes mechanical energy, heat energy, chemical energy, electrical energy, and light energy. The mechanical energy is of two form: the kinetic energy and the potential energy.
Kinetic Energy
It is defined as the energy possessed by the body, by the virtue of its motion.
Thus, every object in motion possess energy irrespective of the object moving speedly or slowly. We can derive the relation for the kinetic energy. Let us consider an object of mass 'm' moving with a uniform velocity' u'. When a constant force 'F' is applied on the object it is displaced through a distance 'S' in the direction of force. The work done by the force is given by,
W = F x S
Let the work done on the object changes its velocity from 'u' to V which produces an acceleration of 'a', then from third equation of motion we have,
\[{{v}^{2}}-{{u}^{2}}=2as\]
Or, \[S=\frac{{{v}^{2}}-{{u}^{2}}}{2a}\]
From Newtons second law, we have
F = ma
Therefore, work done is
W=ma \[\times \] S
Or, W=max v -u
Or, \[W=\,ma\times \,\left( \frac{{{v}^{2}}-{{u}^{2}}}{2a} \right)\]
Or, \[W=\,m\times \,\left( \frac{{{v}^{2}}-{{u}^{2}}}{2} \right)\]
If the object is starting from rest then u=0, hence the work done is given by
\[W=\frac{1}{2}m\times {{v}^{2}}\]
Since this work done is equal to the change in kinetic energy, so the kinetic energy is given by
\[K.E.=\frac{1}{2}\,m\times {{v}^{2}}\]
Potential Energy
It is defined as the energy possessed by the body, by the virtue of its shape and position.
When an object is raised to a certain height its energy increases. This is because of work done on the object against gravity, when it is being raised to a certain height. The energy possessed in such object is called the gravitational potential energy.
Let us consider an object of mass 'm' raised to a height of 'h' from the surface of ground. The force required to raise the object to a height 'h' is equal to the weight of the object more... 
Introduction
In this chapter we shall study about the various concepts of work and energy. All the living organisms needs energy to perform several activities to survive. Work has different meaning in different aspect of life. Scientific notation of the work is that when a force is applied on an object and the object moves through a distance, we can say that work is done. The work done by a force is equivalent to the product of force and displacement of the body in the direction of force.
\[\mathbf{W=F\times D}\]
Where, F is the force and D is the displacement of the object.
When the displacement is in the direction of force, it is called positive work and if the displacement is in the opposite direction of the force, it is called negative work.
For example:
When we throw a ball in the upward direction, its displacement is in upward direction, whereas the force due to gravity acts in downward direction, hence we can say that work done is negative.
\[\mathbf{W=}-\mathbf{F\times D}\]
On the other hand, when the ball falls from a certain height both the displacement and the gravitational force acts in downward direction. Here the work done is positive.
\[\mathbf{W=F\times D}\]
Unit of Work
We know that work is the product of force and displacement. The SI unit of force is Newton and that of displacement is meter, so the unit of work is Newton - meter which is also equal to joule.
One joule of work is defined as the work done by a force of 1 newton, when it displaces a object by a distance of 1 meter in the direction of force. If the displacement of the object takes place in the direction perpendicular to the direction of force, then work done by the force on the object is zero.
For example:
The work done by the lift moving upward direction or by a potter carrying a load moving on a platform is zero.
When the displacement takes place at an angle to the force. Let us consider an object of mass 'm' sliding on an inclined surface making an angle ' Q' with the direction of force 'F' acting on the object. Then the work done by the force on the object is given by \[\mathbf{W=F\times d}\times \mathbf{cos}\,\text{ }\!\!\theta\!\!\text{ }\].
A small child pushes a desk using a force of 10 N. Find the work done by this force if the desk is displaced to a distance of 6 meters.
(a) 40 joules more... 
Introduction
Right from our birth we learn to recognize each other organisms with the help of the sound produced by them. We hear different sounds in our surroundings produced by the different organisms. A small baby recognize his/her parents from their sounds and responds to it. Thus, we can say that sound is a form of energy which produce a sensation of hearing.
Production of Sounds
The most important question that comes to our mind when we study sound is that 'how is sound produced by different organisms?' The correct answer to this question is that whenever something vibrates due to disturbance produced in the medium, the sound is produced. Sound is produced whenever we speak, or whenever we strikes something with the help of hard objects. In each case the sound is produced due to vibration in the medium. The tunning fork is used to produced a specific type of sound. It is a U shaped steel device with a stem at base. Whenever it is strike against a rubber pad cause the prong to start vibration and these vibration produces sound.. 
Propagation of Sound
We know that sound is produced by the vibration in the medium, the substance through which sound is transmitted is called a medium. The medium may be solid, liquid or gas. When an object vibrates, it sets the particle of the medium around it in vibration. The particle do not move from its place. It’s the disturbance that travels through the medium. A particle of the medium in contact with the vibrating object is first displaced from its equilibrium position, and then it exerts a force on the adjacent particles, as a result of which the adjacent particle gets displaced from its position of rest. After displacing the adjacent particles, the first particles comes back to its original position and this process continues in the medium, till the sound reaches our ear.
Thus, a wave is a disturbance which travels through the medium when the particles of the medium starts vibrating. The sound waves are characterized by the motion of particles in the medium and are called mechanical waves. Air is the most common medium through which sound travels. Whenever the vibration starts, it pushes air particles in front of it and creates a region of high pressure. This region of high pressure is called compression. The compression starts to move away from the objects. As the object moves backward, it creates the region of low pressure, which is called the rarefaction. When the object moves backward and forward very rapidly, a series of compression and rarefaction are formed. Thus, sound is propagated through the medium in the form of compression and rarefaction.
What happens during the motion of the wave through a medium?
(a) Particles of the medium moves from one place to another
(b) Energy is transferred in a periodic manner
(b) Energy is transferred from one particle to another at a constant speed
(d) All the statements are correct.
(e) None of these
Answer: (b)
What is sound?
(a) Vibration of particles of the medium
(b) It is a form of energy which produces the sensation of hearing
(b) Particle vibrates along the direction of propagation
(d) A form of disturbance
(e) None of these
Answer: (b)
How is sound produced?
(a) Vibration of particle of the medium
(b) It is a form of energy which produces the sensation of hearing
(b) Particle vibrates along the direction of propagation
(d) Sound is produced due to disturbance created in a medium
(e) None of these
Answer; (d)
What is compression?
(a) The region of high pressure created in the medium when the more... 
Human Ear
Human ear is one of the most important sense organ which enables human to hear the sound distinctly, also to recognize the sound. The human ear is divided into three parts outer ear, middle ear and inner ear.
The outer ear consist of the pinna and ear canal. It collects the sound from the surrounding and transmit it to the middle ear. The middle ear consist of eardrum and three interconnected bones called hammer, anvil and stirrup. These three bones amplifiy the sound several times and transmit it to the inner ear. The inner ear consists of a liquid filled coiled tube called the cochlea. It converts these sounds into electrical signals and then send to the brain via auditory nerve. The brain interprets the sound and reacts accordingly.
The vibrations or the pressure variations inside the inner ear are converted into electrical signals by the______.
(a) Cochlea
(b) Anvil
(c) Hammer
(d) Stirrup
(e) None of these
Answer: (a)
Vibrations inside the ear are amplified by the three bones namely the ______ in the middle ear.
(a) Hammer, Anvil and Pinna
(b) Auditory bone. Anvil and Stirrup
(c) Hammer, Cochlea and Stirrup
(d) Hammer/Anvil and Stirrup
(e) None of these
Answer: (d)
Equations of Motion
The motion of the body moving along a straight line with uniform acceleration can be described by three equations of motion. These equations can be derived as follows.
First Equation of Motion
Let us consider an object moving with a initial velocity 'u'. If it is subjected to a uniform accleration 'a' such that it attains a velocity of V after time 't', then
Acceleration \[=\frac{Final\,velocity\,-\,initial\,ve\operatorname{lo}city}{Time\,taken}\]
So, \[a=\frac{v-u}{t}\]
\[\Rightarrow \,\,at=v-u,\] or \[v=u+at\]
where, v = final velocity of the body
u = Initial velocity of the body
a = acceleration
and, t= time taken
Second Equation of Motion
The second equation of motion is: \[s=ut+\frac{1}{2}\,a{{t}^{2}}\]. It gives the distance traveled by a body in time t.
Let us derive this second equation of motion:
Let us consider an object moving with a initial velocity 'u' and a uniform acceleration "a". Let it attains a velocity V after some time 't'. Let the distance traveled by the object in this time be 's'. The distance traveled by a moving body in time 't' can be found out by considering its average velocity. Since the initial velocity of the body is 'u' and its final velocity is V, the average velocity is given by:
Average velocity \[=\frac{\text{Initial velocity }+\text{ final velocity}}{2}\]
i.e., Average velocity \[=\frac{u+v}{2}\]
Also, Distance traveled = Average velocity \[\times \] Time
so, \[S=\,\left( \frac{u+v}{2} \right)\times t\] …(1)
From the first equation of motion we have, v = u + at. Putting this value of ‘v’ in equation (1), we get:
Or \[S=\,\left( \frac{u+v}{2} \right)\times t\]
Or \[S=\,\left( \frac{2u+at}{2} \right)\times t\]
Or \[S=\frac{2ut+a{{t}^{2}}}{2}\]
Where s = distance traveled by the body in time t
u = Initial velocity of the body and, a = Acceleration
Third Equation of Motion
The third equation of motion is: v- u^ 2as. It gives the velocity acquired by a body in traveling a distance 's'.
The third equation of motion can be obtained by eliminating -f from the first two equations of motion and using the second equation of motion
From the second equation of motion we have:
\[s=ut+\frac{1}{2}\,a{{t}^{2}}\] …(1)
And from the first equation of motion we have :
\[v=u+at\]
Or, \[at=v-u\]
Or, \[t=\frac{v-u}{a}\]
Putting this value of t in equation (1), we get:
\[S=u\,\left( \frac{v-u}{a} \right)+\frac{1}{2}a\,{{\left( \frac{v-u}{a} \right)}^{2}}\]
Or \[S=u\,\left( \frac{v-u}{a} \right)+\frac{1}{2}\,\frac{{{(v-u)}^{2}}}{a}\]
Or \[S=\frac{uv-{{u}^{2}}+{{v}^{2}}+{{u}^{2}}-2uv}{2a}\]
Or \[2as={{v}^{2}}-{{u}^{2}}\]
Or \[{{v}^{2}}={{u}^{2}}+\,2as\]
Where, v = final velocity,
u = initial velocity,
a = acceleration
and s = distance traveled
Graphical Method of Finding Equations of Motion
We can derive the equation of motions using the velocity time graph. Consider the motion more... 
Acceleration
When a bus starts from a stand its velocity increases for some time. When it was at the stand the velocity was zero and after some time it's velocity gradually starts increasing and reaches maximum after some time. Again when it approaches the second stand its velocity gradually decreases and become zero. This means that the velocity of the bus changes during the motion. The rate at which the velocity of the object changes with the time is called the acceleration. Or we can say that velocity per unit time is called the acceleration. It is denoted by 'a'. It is given by,
Acceleration \[=\frac{\text{Change in Velocity}}{\text{Time}}\]
The SI unit of acceleration is metre/sec2 or m/s2
Let us consider the motion of the object along the straight line in the same direction. If 'U' be the initial velocity and 'V be the final velocity, then change in velocity in the time 't' is given by,
\[a=\frac{V-U}{t}\] or \[V=U+at\]
Observations
Uniform Acceleration
Consider a particle moving along a straight line in such a way that its velocity changes in equal amount, in equal time interval. If this happens, then the body is said to be moving with the uniform acceleration.
Velocity Time more... 
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