Gravitational Potential Energy Video Lecture | Physics for JEE Main & Advanced

hello friends this video on gravitation
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8 these chapters we studied potential
energy so potential energy in Sun is the
Chi type of energy which is by virtue of
position of the object right now when I
talk of gravitational potential energy
that means the energy which is by virtue
of position at the same time this energy
is due to the force of gravitation right
so gravitational potential energy can be
defined as potential energy of a body
arising out of the force of gravity that
means when the gravitational force is
acting on a body and that force is
resulting in a kind of potential energy
then that potential energy is known as
gravitational potential energy now if
the position changes on account of force
then change in potential energy is the
amount of work done on the body by the
force that means let us suppose we have
an object say M now if the position of M
changes only because of a particular
force let us suppose if M is changing
its position due to the gravitational
force then we say that the change in
potential energy because of the change
in position of the object is equal to
the amount of work done by the
gravitational force or we can understand
it like this let us suppose this is our
earth it is suppose we have some object
M which was initially at this position
that means which was initially on the
surface of the earth later it was taken
to some point say P or you can take it
like this let us suppose some object was
initially at Point P later it came to
the surface of the earth that is to
point Q and this change in position took
place only because of the four
of gravity that means due to the
gravitational force this object change
its position from P to qu in that case
we would say that the change in
potential energy because at Point P it
would have some potential energy at
Point Q it will have some potential
energy so this change in potential
energy while coming from P to Q will be
equal to the work done by the
gravitational force so we can say w12
where we see that let us suppose this is
position 1 and this is position 2 in
that case the work done in taking the
object from position 1 to position 2 is
equal to the change in potential energy
that is the potential energy at Point 2
minus the potential energy at Point 1 so
what did we learn gravitational
potential energy is potential energy
which is caused due to the force of
gravity now we will go ahead and look at
how to derive expressions for
gravitational potential energy so first
we'll take the scenario where small G
that is the acceleration due to gravity
is constant we will take us in a do
veggie is supposed to be constant let us
suppose this is the earth and we have
some object at Point P or let us call
this point as say ay
now what would be the work done in this
case the work done in this case would be
equal to force into displacement we
already know work done is nothing but
force into displacement so in this case
what would be the force force is nothing
but the gravitational force which is
exerted towards the surface of the earth
that is mg so f will be nothing but mg
and what would be the displacement
displacement would be this height let us
initially it was at point-a later it
came to some point we let us suppose
this way and let us say the height of a
from the surface of the earth was h2 and
the height of point B from the surface
of the earth is h1 so in bringing the
object object is brought from point A to
point B it is supposed the body of mass
M is brought to be from a that means
this object changed its position from A
to B so in this case the displacement
would be this distance so what is this
distance H 2 minus H 1 now we can write
this as mg H 2 minus mgh1 now what is mg
H 2 by definition of potential energy
this is the potential energy at this
particular point at Point a so this
would be B 2 and mg H 1 that is the
potential energy at point B that is V 1
therefore work done in moving an object
from A to B rather this should be A to B
is the potential energy at a - potential
energy at B so the work done is equal to
the difference in potential energies
when we considered that G is constant
that G is not varying in this case right
now let us take the same second scenario
where we consider that value of G is not
constant because in the previous slides
we saw that the value of G changes as
the distance from the surface of the
earth changes so in this case we
consider that scenario that is a little
complex scenario so in this case what
would be the work done in bringing an
object from one position to another let
us say what would be the work done in
this case here again we have this earth
the
I suppose so again in this case let us
suppose this is position 1 this is
position 2 now let us say we determine
the position vector of 2 with our 2
similarly we determine the position
vector of 1 by r1
now here we consider that G is varying
with G is varying with height that means
G is a function of R so in this case W
will be equal to integration of FD ad
from r1 to r2 so what would be F F would
be nothing but G M 1 M 2 PI R square M 1
would be mass of the earth M 2 would be
mass of the object divided by r square
into T RT where TR will be changing from
R 1 to R 2 so this would be equal to
minus G M V into M 1 by r 2 minus 1 by r
1 now this can be written as minus g-m
into M divided by R 2 minus minus g m-e
into m divided by R 1
so we can say this is nothing but
potential energy at R 2 similarly this
is nothing but potential energy at R 1
so here also we can see that the work
done in bringing the object from one
position to another is equal to the
difference in potential energy between
the two positions so in both the cases
we arrived at the same result just that
we went with two different approaches in
the first scenario
that the value of acceleration due to
gravity is constant in the second
scenario we consider the other value of
acceleration due to gravity is not
constant now we will look at the
conclusion about gravitational potential
energy so what did we study about
gravitational potential energy in
general the gravitational potential
energy at any distance R is given by
gravitational potential energy for any
distance R would be given by this is
denoted as V we already know potential
energy is anyways denoted by capital P
so V of R at a distance R at a distance
R would be V of R is equal to minus g
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m-e into M divided by R plus V naught
what does this V naught V naught is the
zero of gravitational potential energy I
mean the baseline of gravitational
potential energy where we considered
that at this point the gravitational
potential energy is equal to zero now
this can be anything most of the time we
considered that the potential energy the
gravitational potential energy on the
surface of the earth is zero so the zero
of gravitational potential energy is
completely upon our assumption there is
no fixed point or no fixed value of
value where the zero of gravitational
potential energy should be zero so in
general we can say that gravitational
potential energy is denoted by minus G M
V into M divided by R plus V naught
where feel or denotes the zero of
gravitational potential energy we also
found that gravitational potential
energy is proportional to the mass of
the particle it is very clear from the
above definition that V of R is
proportional to the mass of the particle
right so these are the two important
conclusion
about gravitational potential energy so
now we will go ahead and define a new
term or introduce a new term to you that
is gravitational potential there is now
we talked about gravitational potential
energy here we will talk about
gravitational potential gravitational
potential due to the gravitational force
of the earth is the potential energy of
a particle of unit mass at that point
that means the gravitational potential
energy of unit mass that means if a
particle is of unit mass then its
gravitational potential energy is known
as gravitational potential so we can say
that gravitational potential is equal to
minus g-m divided by R because the small
M will be equal to 1 so this will be
minus g-m divided by ad so this would be
the expression for gravitational
potential so I hope it is clear please
don't get confused with the similar
terminologies like gravitational
potential energy and gravitational
potential they both are two different
quantities all together thank you please
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