Acceleration due to Gravity above earth surface - Gravitation Video Lecture - Class 11

hello friends this video on gravitation
part 5 is brought to you by exam for
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5 let us suppose that this is our cut we
want to calculate the value of
acceleration due to gravity at some
point which is at a distance H from the
surface of the earth let us suppose we
want to calculate the value at some
point P which is at a distance H from
the surface of the earth now this is the
centre of the earth so this distance is
R that is the radius of that from this
point till the centre this is the radius
and this is the object which is located
at a height H and it is suppose the mass
of this object is M 1 M 1 is the mass of
the object or M is the mass of the
object let us say not to complicate it
further we say that M is the mass of
this object fine now here also let us
try to calculate the force of
gravitation between this object m and
the earth the force of gravitation on
this object M due to earth will be
capital G m1 m2 divided by R squared
what is R R is the distance between the
two objects that means distance of this
object M from Earth so what will be that
distance R e + H so this would be AI e +
H whole square right so this is the
force of gravitation
on the surf object M due to the earth so
we can say what would be the value of G
now again here we are calculating G of H
that means the value of G at a height a
above the surface of the earth so this
value so G will be equal to F by M that
means this will be equal to g m-e
divided by re plus h whole square right
now in this case let us suppose we take
out our e as a common so this would be 1
plus h by IE whole square right so we
have taken out our t common from inside
so i am left with 1 plus h by IE whole
square now let us if you consider if you
think it very practically this distance
H will be very small when compared to
the radius of the earth you imagine this
scenario in real life radius of the
earth earth is so huge so radius of the
earth is also very huge but when we
consider the height of an object from
the surface of the earth that will be
very small when compared to the radius
of the earth that means this H will be
very very small when compared to the
radius of the earth therefore we can
apply binomial theorem how do we apply
binomial theorem we can write the above
expression as g m-e
divided by r e square this you leave as
it is so this into 1 plus h by r e to
the power minus 2 because i took it to
the numerator
now since h is very very less than r e
that means this entire term will be very
very less than 1 that means it will be a
very small term so in this case we can
apply a binomial expansion so we will
expand it binomial so what do how do we
expand something binomially the binomial
expansion expansion says binomial
expansion you must have studies all
these things in your
it's binomial expansion see is that 1
plus X to the power n can be written as
1 plus n X plus n into n minus 1 by
factorial X square and so on like this
is how the binomial expansion is done so
in this case since H is very very less
than RT we can expand this term binomial
but we will consider only the first two
terms we will neglect the higher terms
so expanding this in binomial so what do
we get we get g m-e by r in square this
we believe as it is and this will be 1
plus n X what is n here n is minus 2 so
this will be 1 minus 2 and X is H by r
in so this would be this now as I
already told you previously also what is
GME by re square it is nothing but the
value of acceleration due to gravity G
on the surface of the earth so this
would be G into 1 minus 2 H by re now
what is this what we'll be calculating
we were calculating the value of G at a
height H above the surface of the earth
so we saw that how does the value of
acceleration due to gravity varies on
the surface of the earth above the
surface of the earth and below the
surface of the earth so I hope it is
clear to you see in this case the in the
derivations we are doing nothing but
applying simple mathematics all you need
to do is it is very much important to
learn and to remember these formulas
deriving this formula is not a big deal
because once you understand the
mathematics which we are using behind
this it will be very easy for you to
derive such things but remembering the
formula is important so that you can
solve the problems quicker and easier
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