Check the Note here: Force - Science Notes Class 10
Unit-1 | Gravitational Force | Class-10
Overview: Gravitation is an attracting force existing in all the
objects in the universe due to their masses. The force which attracts
every object towards the center of the Earth is called gravity. Sir Isaac
Newton (1642-1727) (an English Mathematician and physicist) discovered
gravity. Also, he proposed the universal law of Gravitation.
Force:
Force is an external agency that changes or ties to change the position of
an object. In general words, Force is the push or pull acting on an
object.
The SI unit of Force is Newton (kgm/s²) and C.G.S. unit of Force is
Dyne (gcm/s²).
Relation between Newton and Dyne:
We know,
1 Newton = 1 kg × 1 m/s² [ F = ma ]
= 1× 1000g × 1 ×100cm/s²
= 1000g × 100cm/s²
= 100000 g cm/s²
= 10^5dynes
So, 1 Newton = 10^5dynes
Gravitation (Gravitational Force):
Gravitational Force is the force of attraction between two bodies in
the universe due to their masses. It is always the attracting
force.
Newton's universal law of gravitation:
According to Newton's universal law of gravitation,
every object in the universe attracts every other object with a
force which is called gravitational force. This gravitational force
is (i) directly proportional to the product of their masses and (ii)
inversely proportional to the square of the distance between their
center.
This law is called the universal law because it is applicable to every
body in the universe regardless of their shape, size, mass, distance
between the centers and time.
Prove: F = Gm1.m2 ⁄ r²
Let, the distance between centres of the two objects A and B of masses
m1 and m2 respectively be 'r'. If F is the gravitational force between
them then, according to the Newton's universal law of gravitation:
F ∝ m1.m2 .................(1)
and
F ∝ 1/ r² ......................(2)
Combining equations (1) and (2), we get,
F ∝ m1.m2 / r²
Therefore, F = Gm1.m2 /r²
Where, G is the universal gravitational constant.
#proved.
What happens to the force of gravitation if masses of the bodies
are doubled keeping the distance between them constant?
Solution:
We have,
Gravitational force (F) = Gm1.m2 /r² ....(i)
According to the question,
Mass of body A (mA) = 2m1
Mass of body B (mB) = 2m2
Distance between A and B = r
Then,
F1 = GmA.mB /r²
[Where F1 is the new gravitational force]
or, F1 = G2m1.2m2 /r²
or, F1 = 4 Gm1.m2 /r²
So, F1 = 4F [ from equation (i)]
Hence, when the mass of both the objects is doubled keeping the
distance between them constant then the gravitational force will be
increased by four times from the initial value.
Practice yourself:
What happens to the force of gravitation if the masses of the
bodies are halved keeping the distance between them constant?
What happens to the force of gravitation if the masses of the
bodies are doubled and the distance between them is also
doubled?
Universal Gravitational Constant (G):
The Universal Gravitational Constant (G) is equal to the force of
Gravitation between two bodies of unit masses (i.e. of 1 kg each)
separated by a unit distance (i.e. 1 m).
SI unit of G is Nm²/kg². Its value is 6.67×10^(-11) Nm²/kg².
Its value is always constant because it does not depend upon the
masses and distance of the bodies along with the variation in
their (bodies and medium separating those bodies) characteristics.
It is a scalar quantity.
Gravity or Weight:
The force which attracts every object towards the center of the
Earth is called gravity or weight of the body. The SI unit of
gravity is Newton (N).
Effects of gravity:
Gravity makes human life very easy. Due to the earth's gravity,
we can freely walk, stand, play and perform other activities.
Any object that is thrown upwards again returns to the earth's
surface. All types of construction of roads, bridges, building
are possible.
Mass:
The total amount of matter contained in a body is called its
mass. Its SI unit is kilogram (kg). It is a scalar quantity. It
is measured using a beam balance. Its value is constant all over
the universe.
Acceleration due to Gravity (g):
Acceleration due to gravity (g) is the acceleration produced on a
freely falling body due to the gravity present in the Earth.
Its SI unit is m/s² and its average value in the Earth's surface
is 9.8 m/s². It is a vector quantity. Its value changes from place
to place.
Relation between radius and acceleration due to gravity of the
earth:
Let M be the mass of the earth with its radius R. Suppose the
body on the surface of the earth has mass m..
Then,
According to Newton's universal law of gravitation, the force
of attraction between them is given by:
F = GMm /R^2 .......... (a)
Here, F represents the force by which the body is attracted
towards the earth. So F represents the weight(W) of the object.
Then, equation a becomes:
W = GMm/R^2 ..........(b)
But we have, from the second law of motion,
W = mg ......................(c)
Hence, from (b) and (c), we get;
mg = GMm/ R^2
or, g = GMm/ R^2m
So, g = GM / R^2
So, you can calculate acceleration due to gravity with the
above expression.
Variation in the value of acceleration due to gravity (g):
Variation because of the shape of the Earth:
g ∝ 1/R²
This is the reason the value of 'g' is more than in the
equatorial region.
Variation with the height from the surface of the Earth: g' =
GM / (R+h)²
This is the reason the value of g at higher altitude is less
than in the areas of lower altitude.
Variation with the depth of the Earth's surface: g' = (1 -
d/R).g
From this relation, as the depth (d) increases, the value of
'g' also decreases.
Gravitational field and gravitational force intensity:
The area around a heavenly body up to which the influence of
its gravitational force can be felt is called gravitational
field.
Gravitational force intensity at any point is the amount of
force experienced by a unit mass kept at that point in the
gravitational field of the heavenly body.
Gravitational field intensity (I) = Gravitational Force
Experienced (F) / Mass (m)
To calculate the gravitational field intensity, we use the
formula,
Gravitational field intensity (I) = Universal Gravitational
Constant (G)x Mass of body(M) / Radius of the body
(R^2)
i.e. I = GM/ R^2
Therefore, this is numerically equal to acceleration due to
gravity.
Free Fall:
When an object is falling towards the surface of the earth
under the gravitation force only and without air resistance,
then the body is said to be in free fall.
Weightlessness:
Weightlessness is the state in which the resulting weight
of the body is zero due to the zero reaction force of the
earth or other heavenly bodies. It occurs only when the
acceleration due to gravity is zero.
Let us assume that we are ascending upwards in an elevator
at an acceleration (g') that equals the downwards pull
exerted by the gravity (g). Since, these two forced are in
opposite directions and equal, they can each other. So,
reacting force (or resultant force) = g - g' = g - g =
0
We know,.weight = mass × acceleration due to gravity = mass
× 0 = 0.
Thus, the body is said to be weightless. And, such condition is
called weightlessness. There are many more cases for weightless,
as well.
Solved Numericals:
The mass of Jupiter is 1.9 x 10^27 kg and that of the sun is
2 x 10^30kg. If the distance between them is 78 x 10⁷ km, find
the gravitational force between them.
Solution:
We have,
Jupiter's mass (m1) = 1.9 x 10^27 kg
mass of Sun (m2) = 2 x 10^30 kg
distance between them (r) = 78 x 10⁷ km = 78 x 10⁷
x 10³ m = 78 x 10^10 m
Now,
gravitational force (F) = Gm1m2 / r²
= 6.67 x 10^(-11) x 1.9 x 10^27 x 2 x 10^30 / (78 x
10^10)²
= 4.166 x 10^23 N
If the mass of a man is 70kg, what would be his weight on the
moon? Find the mass of the same person on the Earth as
well as on the moon.
Solution:
mass(m) = 70kg
acceleration due to gravity on moon(gm) = 1/6 * g = (1/6*
9.8)m/s^2 = 1.64m/s^2
So, weight of the man on the moon (W) = m * gm = 70* 1.64
= 114.3N
His man on the earth and the moon would be the same. i.e.
70kg.
What is the reason behind the weight of body is more at poles
than in equator?
Why is it difficult to lift a big stone than a small one?
Answer: Gravitational force is the weakest force. Its magnitude
depends largely upon the mass of the substance (or object). A bigger
stone has comparitively larger mass than the smaller one. Thus,
magnitude of the gravitational force acting on the bigger stone is
greater than the smaller stone. This means, the bigger stone is
pulled more heavily by the Earth's gravity than the smaller one.
When we try to lift both stones to the same height, more force has
to be exerted on the bigger stone in order to tackle the larger
magnitude of downwards pulling gravitational force. Hence, it is
difficult to lift a big stone than a small one.
Simply, due to heavier mass of bigger stone, it is pulled downwards
by the Earth's gravity more than the smaller one. As a result, when
we try to lift it up, the gravitational force acts as a barrier and
makes it difficult to lift a big stone than a small one.
Calculate the gravitational force between two bodies of
masses 750 kg and 1500 kg if they are placed at 500 m
distance? (Ans: 3.0 x 10^(-10) N)
The masses of the sun and the earth are 2 x10^30 kg and 6
x10^24 kg respectively. Find the gravitational force between
them if the distance between their centres is 1.5 x10^11 m.
(Ans: 3.56 x10^22 N)
If you neglect the air resistance, on falling two objects
with masses 50kg and 10kg respectively from equal heights,
which one would touch the ground first? Give reason in support
of your answer.
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