Test Papers – ICSE – Class – X
Physics 02, Gravitational and Spring Potential Energy,Work Energy Theorem
So there is one special thing called potential energy that we call conservative force. So write,
relation between conservative force and potential energy. Relation between conservative
force and potential energy. Okay, class, write now. Change in potential energy is equal to
minus work done by conservative force, okay. Now, from here we will create gravitational
force potential energy (1:36) Conservative force work is multiplied by minus 1 then we will
go towards change in potential energy. So this is gravitational potential energy. Let’s say an
object is moving from one point to another point under the gravitational effect. Like see this,
this is earth surface. One object is here with m mass, let’s say it’s height from the ground is
h1. It moves to this location, whose height from the ground is h2 and between these two
points the vertical separation is capital H, okay. Now, we are moving from point 1 to 2, let’s
say along this path. Now, let’s calculate work done by gravity in this particular path. See
carefully, if we apply a little effort then you will see an interesting thing, we will get two
things in this entire derivation. One is constant force work done, special property of work
done by a constant force and second thing we will see develop gravitational potential energy
also, okay. For complete motion we have observed one thing that on this block one constant
gravitational force is applied downwards, right. Force is constant, when we will tell force is
constant when its direction and magnitude are same, okay. Now, see class by using this
idea, I will write gravitational force like this, okay. Now, this is the first point and this is the
second point. From first point to second point we will travel through an arbitrary path or
track, done. Now, what we did, in the whole displacement, I will select in the entire path I
will select displacement ds, okay. Through the track or path which we are moving, we
selected a small displacement, ds. Yes or no? Now, see, our displacement is a vector
quantity. So, see carefully, what I will do is, I will cut this displacement into two pieces. I will
magnify this displacement. I can see a straight line, ds, this is the displacement vector. Now,
I will make the component of this displacement in the direction of force and perpendicular
to the force. In the direction and perpendicular to the direction, we will make the force as
component. ds, perpendicular to force and ds parallel. See, this is a vector quantity, I can
make it component anywhere and anyhow. Now, I know that force is always vertical here.
So, what I did, I made one component vertical and other component horizontal. One
horizontal component and other vertical component, two pieces, okay. I deliberately divided
the displacement into two pieces, one horizontal and other vertical. That means, this
displacement ds can be written as ds perpendicular plus ds parallel. Let it be any arbitrary
path, selected a small displacement on it and divided that small displacement into two
pieces, ds perpendicular and ds parallel, perpendicular to force and parallel to force, okay.
That means, now I will write, work done by my constant force, what will it be – f dot ds? And
now what I will do is, I will write ds as perpendicular and parallel. Tell me one thing, if I make
two pieces of this full integral, ds perpendicular, ds perpendicular means force and angle
between this force, how much it is, 90 degree. That means the work done value is zero. That
means finally the total work done is F dot ds will be parallel. And if it is constant force then
displacement is useful only when it is parallel to force, okay. The displacement which is
perpendicular to the force in that value will be zero. Okay, force value is constant, so I can
keep force outside integration – ds parallel. And ds parallel can be written as delta s parallel,
the total displacement. That means constant force work done can be written directly, if I am
clear that force is constant and the constant force whether it is conservative or not, the
work done can be written directly. How much? F dot product with the displacement which is
parallel to force. That means in direction of the force or opposite direction of the force. And
if I see carefully, I can simplify this plus minus F delta s parallel. Plus minus F delta s parallel,
why did it put plus minus here, so that dot product can be eliminated and if it is parallel then
the angle between them would be zero degree or 180 degree. When will I apply plus, when
they are in the same direction and when will I apply minus, when they are in opposite
direction. Okay, so we have simplified work done by constant force. As long as you know the
force is constant, you can write straight away work done as plus minus F delta s parallel. In
this full.
Physics 04, Force Potential Energy Relation and P E Curve
Okay, find the maximum elongation. Block is released from rest, block is released from rest
and the spring is at its natural length. Spring is at its natural length. Class, let us discuss one
thing. It was released with zero initial velocity. When will there be maximum elongation?
When it will stop moving. You should understand that the block will move and maximum
elongation means no further elongation. That means block has stopped and will come back.
And during that process this block goes down x distance and this spring gets elongated by x
amount. This problem is spring based, that is why we have to apply energy analysis. So, I will
take this as initial and this as final. Block is moving in vertical plane. Means we have to count
gravitational potential energy. So, let’s take this as a zero potential energy reference line and
in between 1 and 2, I will apply initial kinetic energy, initial potential energy and initial spring
potential energy, all three are zero because in which condition was the spring in the
beginning, rest, natural length. Final kinetic energy zero, final potential energy will it be mg
by, sorry, minus mg x, yes, and what is spring potential energy? K by 2 x square, because if
this goes down then our spring will be elongated, yes or no. So, x is equal to 2mg by k. How
many of you did it right? Now, we will mix the previous example with this example. We will
do one thing, we will search for a special position, such a position where this block has come
down x naught. And this is the position where the weight is applied on this block and the
spring force which is applied on top both are equal. We are assuming that zero force
condition is, you can call it as equilibrium condition, it arrives, when your block comes down
x naught distance, then mg is equal to x naught that means what will the value of x naught
be? Mg by K, right, that means x naught is the elongation at which the force on the block is
zero. What is x naught? Elongation for zero force. Ask, if you have any doubt. We just
assumed that x naught is the elongation because we thought in between force may be zero,
we don’t know and now there is x naught and this is clear also, see this value and see this
value, isn’t it double. Suppose, if I say maximum elongation is there that is 2 times zero force
elongation. Tell me, if it will work or not, we saw this in the previous example. See, last class
last example very carefully. What will be the elongation of zero force? See, last to last
example, F by K and how much is the maximum? Isn’t it, class, this funda is working. Now,
we will see what is happening in this funda basically.
See, there are two forces on the block. One is mg and other is spring force, right. When
value of elongation is less than x naught, that means the block is in this domain. If block is in
this domain, then you will see mg is greater than spring force. So, when does mg becomes
equal to spring force when the value of x is x naught. If value of x is less than x naught, then
mg will be greater than spring force, yes or no. Means where will be the resultant force
applied – Downward direction. And velocity is also down and even acceleration is also down.
Means the speed of our block is increasing, yes or no. That means in this region velocity is
downwards and acceleration is also downwards, so velocity will keep on increasing, okay.
The point has crossed this block and has come in this region. So, in this condition what will
happen? The value of elongation will be more than x naught. See, this value of kx is more
than kx naught. And kx naught is equal to mg, yes or no. That means this time the spring
force value will be greater than mg. If the value of spring force is greater than mg, then the
resultant force acting on the block will act in upward direction. Velocity downward,
acceleration upward, now the block will (8:40). What happens actually, in this question also,
the answer didn’t come as mg by k. In this the answer is 2mg by k because when force is
zero in that condition the force doesn’t stop, before that the block is getting accelerated and
accelerated.
Chemistry 02, Stoichiometry and Limiting Reagent
We will start, friends in the previous lecture we have discussed what are atoms, what are
molecules, how to calculate total number of atoms and how to calculate total number of
molecules. If one sample is given we can find out many entities are present in that sample
let it be molecules, or individual atoms or we can also take mass, if we are told the number
of atoms, so we can calculate, the mass of the sample itself. We have to use the same
problem again and again. The number of entities or the number of atoms or number of
molecules is equal to the mass of the sample divided by the, yes, atomic mass or molecular
mass or mass of one entity. That could be any entity, it could be ion, atom or a molecule. We
can take anything. Till now you studied that how we interpret things by one mole atom. One
mole atom implies 0.622 into 10 raise par 23 atoms. Now, see you will be able hearing one
more language. When we are talking about the sodium case, let’s say we are talking about
sodium, or silicon. We don’t prefer sodium because when we write Na it gets confused with
Avogadro’s number. Let us say, we will talk about 28 grams of silicon. What does this imply?
What does this imply, how many atoms, do I have? One, one mole atom, or it is, it is correct.
1 mole atom or it is equal to Avogadro’s number of atom of silicon. Okay, if I give you a 28
gram atoms of silicon. Understand, that gram atom also means mole. Gram means normal
weight but gram atom means mole atom, gram molecules means mole molecules, gram ion
means mole ion. Generally what we do is, when we define things in grams with that
particular term, we refer to the mole of that quantity. For example, 28 gram atoms of silicon
implies 28 mole atoms of silicon and that implies 28 times Avogadro’s numbers of silicon.
There is huge difference. 28 gram of silicon is 1 mole atom but 28 gram atom of silicon again
implies 1 mole atom. Similarly, if I say, 44 gram of carbon dioxide implies how many mole
molecules, 1 mole molecule. Okay, what about, if you say, 44 grams molecules carbon
dioxide. This is definition. Yes, this is definition, this is how you define atom or atom gram
molecule. So, you say 44 gram molecules of carbon dioxide implies 44 mole molecules, okay.
Okay, similarly, if I say, here you correlate with this, let’s say 23 gram sodium ion implies 1
mole sodium ion or I can say that here, 23 gram ions of sodium 23 moles of sodium ion.
Everybody understood this. So, in this type of interpretation you will be asked data about
gram atoms, gram molecule and gram ions. And that is also interpreted as mole atoms,
mole molecules or mole ions.
If I ask you one simple question, what is the difference between 1 gram of oxygen and 1
gram of atom of oxygen? Now, what will you say? Correct, 1 gram atom. Repeat once more,
1 gram of oxygen implies mass of sample of oxygen is equal to 1 gram whereas here, mass of
sample of oxygen will imply, sample of oxygen, it is 1 mole and what is mass of 1 mole
oxygen is 16 gram. Everybody understood this. This differentiation we will make, this you
can keep in mind easily. Mark this, mark this entire thing. This is important, this is another
way of interpretation of mole. Okay, mole is also defined as gram entity of something. Mole
is also defined as gram entity of something. Everybody wrote it down, mark it. Then we will
start study of chemical reactions. Everybody understood the meaning now. What is the
meaning of gram of something, gram atom, gram molecule or gram iron. Everybody wrote it.
Okay, now let’s start the study of chemical reaction. First of all define what are chemical
reactions? Is preserved and what actually occurs, yeah tell. Products, reactant combined to
give products or like you said rearrangement of atoms. So, let us write, write rearrangement
of atoms between various molecules of reactants. Rearrangement of atoms, rearrangement
of atoms between various molecules of reactants, rearrangement of atoms between various
molecules of reactants to form new molecules of products, between various molecules of
reactants to give new molecules of products is called chemical reaction, is called chemical
reaction. Rearrangements of atoms between various molecules of reactants to form a new
molecules of products is called chemical reaction, okay. Write ahead, since atoms are
rearranged since atoms are rearranged they remain conserved. Since atoms are rearranged
they remain conserved and therefore the mass is also conserved. You already know these
two things, conservation of atoms and conservation of mass, okay. Since, atoms are only
rearranged, the atoms are conserved and their mass is also conserved. So, therefore we say
in a chemical reaction mass is conserved.
Okay, now let us define the term Stoichiometry. What is Stoichiometry? Okay, so you write
here, it is a study of chemical reactions, it is a study of chemical reactions, it is a study of
chemical reactions and calculation related to it. Study of chemical reactions and calculations
related to it, okay. Now, I will write a chemical reaction here which we will be repeating
again and again in the next few examples, okay. And through that you have to explain to me
some interpretations, okay. SO2 plus O2 combines to give you SO2. This we know as a
reaction, okay, and if we talk about this reaction because there is something missing in this
reaction, correct. There is no balance. So, we say currently the equation is.
Chemistry 01 , Atoms and Molecules
Mole and Equivalent Concept:-
In the beginning we will be targeting only the mole concept. And we will try to understand
only the mole concept. We will not bring into the discussion of equivalent concept, this will
be only done when we have completed the portion of mole concept. But both are parts of
Stoichiometry calculation, so there is no need to think much about it whether it is
independent or combined. They are combined, they are independent, you can say they are
both. So, there is no need to think about it much.
Again, we start off with the first and foremost very simple definition, mole concept. In mole
concept you will be actually doing the calculations. You will be, you know weighing a sample,
calculate mass or you will be counting that in this how many entities are there, maybe
molecules, maybe irons, maybe atoms, things like this you will be calculating. Okay, we will
do something like this. You know, mostly we are afraid of mole concepts, why, because
there are more calculations in it, and you feel that now we will have to do these dreadful
calculations and how will we do that. Remember, if you overcome the fear of calculations
then mole concept is very, very easy, nothing complicated, okay. There are many systematic
thought process questions, things are not as complicated as it looks. Yeah, the steps may
increase, maybe one problem would be solved in one step, maybe in two steps or maybe in
three steps. But the process is very easy in mole concept. Be comfortable, whoever knows
addition, subtraction, multiplication, division and unitary method, they know mole concept
also. If someone is unable to do these then they will have little problems. I have only one
request for them, the ones who have problems while doing calculations, improve your speed
on calculation and be confident with calculation. Otherwise mole concept is a very easy
chapter, okay.
Now, in this particular chapter we will start off with the definition of Atom. Yet again, we
start with the definition with atom, which we had discussed in atomic energy. So, tell me the
definition of atom. What is the definition of atom? It is the smallest indivisible particle of
matter. According to which theory, we will write here. You write the definition of it again.
Atom is the smallest part of an element, atom is the smallest part of an element, atom is a
smallest part of an element that can participate in a chemical reaction. Atom is a smallest
part of an element that can participate in a chemical reaction. When we are talking about
chemical reaction we say that there is one more type of reaction associated. There are two
types of reactions, one is a chemical reaction, the other is a radioactive reaction, okay.
Radioactive reaction is also called as Nuclear reactions, okay. So, what we say here is,
suppose I have a reaction here, HCL plus NaOH and they react, what will happen? Okay, here
identity of elements is maintained. Here one HCL is there, two H and one oxygen, similarly,
here one Na, one CL, two H and one oxygen. Similarly, if I take here, let’s say silver nitrate
plus NaCL, so what do I get, AgCL plus NaNO3, this is the example of double displacement
reaction. So when we see this sort of example, we call them as normal chemical reaction. In
which chemical identity of the element is preserved, it is not changed. Whereas in
radioactive reaction, let’s say we pick up uranium 92, the uranium atomic number is 92 and
its isotope, if considered particularly, it is 238. Let’s say it emits out an alpha particle, now
what is an alpha particle? Helium 2 positive nuclear, which we say helium 2 positive particle
is emitted. Whenever we write any radioactive reactions we never write the charges, we just
write the elements which are emitted from there. We say, suppose helium is emitted, in
helium there are two protons and two neutrons, agreed. If we say from this how many
protons are emitted from this uranium nucleas, 2 and how many left, 90 and what is the
reduction in mass number. 4 because 2 protons and 2 neutrons. So, I will write here, 230 and
if you remember this 90 stands for thorium, okay. So, uranium and thorium and with that
what was given out, so you told alpha particle was given out and you got the thorium, okay.
And suppose we say some energy was also emitted out. That is in the form of Gama
radiations, okay. Now, see this equation and compare it with this equation. Have the identity
of elements been preserved? The nucleus itself has changed, so we say that there are two
types of reactions. In which case we will say that atom is a smallest part which can
participate in a reaction, in a chemical reaction not in a radioactive reaction. In radioactive
reaction, all the atomic particles participate like alpha particles, neutrons, protons things like
these participate. So we have to differentiate between both of them.
I will give you one more example of reaction. Do you remember discovery of neutron. Yes, in
(6:53) and with what we have confirmed with, beryllium. With what we had bombard it,
alpha particle and what was made out of it, carbon and what was emitted. Again identity of
elements had changed. What had happened? This is also a nuclear reaction. We will mark it;
let us say beryllium 4, 9, helium 2, 4. Now you see, you try to conserve the mass number and
atomic number. 4 plus 2, 6 carbon. How much is 9 plus 4, 13 total mass number. But we say
isotope of carbon is made of 12 number and to conserve mass number what will be emitted,
neutrons. So these types of reactions are called as radioactive reactions. For us, where is the
atom in the whole concept, only in the case of chemical reactions. Only in these cases you
will call it to be the smallest part. It’s only in the case of chemical reaction, never in the case
of radioactive reactions or nuclear reaction. Did everybody understand this? So that is
important, so keep this in mind. From helium to, yeah, yeah, like that you can choose
anything. You can do many nuclear reactions. If you bombard on isotopes of beryllium you
will get some other elements. We are taking just couple of examples to understand what are
the examples of nuclear reactions. In one case, alpha is emitted and in another case alpha
has been absorbed. There are many types of examples. We have not talked about beta
particles, positron emission, electron emission. We are just taking simple analysis which is
not complicating our analysis. Everybody understood this thing, okay.
Now, if we talk about, we defined what is an atom. But we have to do calculations and to do
calculations, I have to count. There are two types of counting procedures, we can count as
discreet quantity. Let’s say you are students who are counting as discreet quantity. For
example we will start counting, 1,2,3,4,5,6,7,8,9,10, we count like this. This is one way.
Second I will collect information.
