2. Introduction about Gravity
Dearchildren beforestarting thischapter, I would like toask few
questions;
When you dropa stone fromacertain height then itwill falls
towardsearth surface. Why?
When you throwa stone upward then it’scome back toearth
surface. Why?
⚫ Theanswerof theabovequestion is Gravitational force.
Gravitation, is a natural phenomenon by which all things with
mass or energy including planets, stars, galaxies, and even light
particles are broughttoward (or gravitate toward) oneanother.
while On Earth, GravitygivesWeight tophysical objects.
3. Universal Law of Gravitation
The Law of Universal Gravitation states that every object of
mass in the Universe attracts every other object of mass
with a forcewhich is directly proportional to the product of
two masses and inversely proportional to the square of the
distance between theircenters.
Let two object having mass m and M and their distance
between them from their centre is d.
According to Newton Gravitational law
4. Cont…… from page-3
Let mass of small object is m and mass of big object is M and distance between
them is d.
F 𝖺 M × m ………………………(1)
and inverselyproportional to the squareof the separation between theircenters
F 𝖺 1/d .....................................(2)
Combining above twoequation
Where G is the constant of proportionalityand is called the Universal Gravitation
constant.
Theaccepted value of G is 6.673 X 10–11 N m2 kg–2
2
6. Que. How does the forceof gravitation between twoobjectschange
when thedistance between them is reduced to half ?
Answer. …………(1)
Force is inversely proportional to square of distance between two
object.
d is replaced byd/2
Hence force Increases fourtimes.
How does the forceof gravitation between twoobjectschange
when thedistance between them is reduced to three times ?
Ans- d is replaced byd/3
Forceof attraction increases 9 times.
7. ⚫ Howdoes the force of gravitation between twoobjectschangewhen the
distance between them is increases to threetimes ?
Ans- d is replaced by 3d Squaring 9 times
Forceof attraction reduces 9 times.
⚫ Howdoes the forceof gravitation between twoobjectschangewhen massof
oneobject is increases to threetimes ?
Ans- m is replaced by 3m
Forceof attraction increases 3 times
⚫ How does the force of gravitation between two objects change when the
distance between them is reduced to threetimes, while massof oneobject is
increases to threetimes?
Ans- m is replaced by 3m and d is replaced byd/3
It gives Forceof attraction increases 27 times
8. The universal law of gravitation successfullyexplained several
phenomenawhich were
believed to be unconnected:
(i) The force that binds us to theearth.
(ii) The motion of the moon around theearth.
(iii) The motion of the planets around the Sun.
(iv) The tidesdue to the moon and sun.
Importance of Universal law of Gravitation
9. Kepler’s laws:
Johannes Keplerderived three laws, which govern the motionof planets.
Thesearecalled Kepler’s laws. Theseare:
1. The orbit of a planet is an ellipse with the Sun at one of the foci, as
shown in the figuregiven below. In this figure O is the positionof the
Sun.
2. The line joining the planet and the Sun sweep equal areas in equal
intervalsof time. Thus, if the timeof travel from A to B is the same as
that from C to D, then theareas OAB and OCD areequal.
3. Thecubeof the mean distanceof a planet from the Sun is proportional
tothe squareof itsorbital period T. Or, = constant.
10. It is seen that a falling apple is attracted towards the
earth. Does theappleattracttheearth? If so, wedo not
see theearth moving towardsan apple. Why?
According to the third law of motion, the apple does
attract the earth. But according to the second law of
motion, foragiven force, acceleration is inversely
proportional to the mass of an object. The mass of an
apple is negligibly small compared to thatof theearth.
So, we do not see the earth moving towards the apple.
Extend the same argument for why the earth does not
movetowards the moon.
11. State the Universal law of Gravitation .
Give the SI unitof Universal Gravitation constant.
Write the formula to find the magnitude of the gravitational force between the Earth and an object on the
surface of the earth.
Howdoes the force of gravitation between two objects change when the distance between them is reduced
to one fourth?
What happens to the force between two objects, if
(i) The massof one object is half?
(ii) The distance between the objects isdoubled and tripled?
(iii) The masses of both objects are doubled?
Whatdo we call thegravitational force between the earth and object?
What is the importance of universal lawof Gravitation?
The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon
with a force that is greater or smaller or the same as the force with which the moon attracts the earth?
Why?
What is the magnitude of the gravitational force between the earth and 1 kg object on its surface? (Mass
of theearth 6 x 1024 kg and radius of the earth is 6.4 x 106 m.
12. Free fall
Whenever objects fall towards the earth under the force of
gravitation,we say that the objects are in free fall.
Is there any change in the velocity of falling objects?There will be a
change in the magnitude of the velocity
.Any change in velocity
involves acceleration.Whenever an object falls towards the earth,
acceleration is involved.This acceleration is due to the earth’s
Gravitational force.Therefore,this acceleration is called the
acceleration due to the gravitational force of the earth (or
acceleration due to gravity).It is denoted by g.The unit of g is the
same as that of acceleration,that is,m s–2
13. During the free fall velocity of an object linearly increases with
time.ItmeansfreefallisanexampleofNon uniform velocity
14. Relation between ‘g’ and ‘G’
Let two object one of them is Earth having mass Me radius of earth
Re, so according to universal law of gravitation
F= Gme.m/Re^2
Then according to Newton second law,force acting on the small
object mass(m) is given by
F= mg
18. Equation’
s ofMotionunder theinfluenceof
accelerationdue to gravity
As g is constant near the earth,all the equations for the uniformly
accelerated motion of objects become valid with
acceleration a replaced by g,hence
The equations will be
where uandvaretheinitialandfinalvelocities and s isthe
displacement covered in time,t.In applying these equations,we
will take acceleration,g to be positive for downward motion.
The acceleration,g willbe taken as negative for upward
motion.
20. Mass andWeight
Mass is a measure of the number of atom or amount of
matter containing in an object.
SI unit of Mass is Kg.
While weight is a Force of attraction provided by Earth on
unit mass object.
Weight = Mass xAcceleration due to gravity
Or w = m.g
SI unit of weight is Newton
22. poleto
How does the value of g changes form
equator?
We know that,
i.e g α 1/squareof radius of Earth
As the earth is an oval shape, its radius near the equator is more than its
radius nearpoles. Since fora source mass, the accelerationduetogravity is
inversely proportional to the square of the radius of the earth, it varies with
latitudedue to the shapeof theearth.
gp/ge = R2 /R2
e p
Wherege and gp are theaccelerations due togravity at equatorand poles,
Re and Rp are the radii of earth nearequatorand poles respectively
.
From theabove equation, it is clearthatacceleration due togravity is moreat
poles and less at equator. So if a person moves from the poles to equator his
weightdecreasesas thevalue of g decreases.
24. Amit buys few grams of gold at the poles as per the instruction of oneof his friends. He
hands over the same when he meets him at the equator. Will the friend agree with the
weightof gold bought? If not, why?
Let m be the mass of thegold bought.
suppose theaccelerationdue togravityat poles and atequator
be g and g’ respectively. Accelerationdue togravityat poles is slightlygreaterthan
thatatequator.
i.e g α 1/squareof radius of Earth
Wp=mg
We=mg’
∴ Weightof gold at poles
Weightof gold atequator
But as g > g’ ⟹Wp>We
Hence theweightof gold is slightly less atequator.
So the friend will not agreewith Amitabout theweightof gold bought.
26. Example-1
A carfallsoff a ledgeand drops to theground in 0.5 s. Let g = 10 m s–2 (for
simplifying the calculations).
(i) What is its speed on striking theground?
(ii) What is its average speed during the 0.5 s?
(iii)How high is the ledge from theground?
Solution:
Solution:
Time, t = ½ second
Initial velocity, u = 0 m s–1
Accelerationdue togravity, g = 10 m s–2
Accelerationof thecar, a = + 10 m s–2 (downward)
(i) speed v = u + a t
v = 0 + a t
v = 10 × 0.5 s
= 5 m s–1
28. Example-2
An objectweighs 10 N when measured on the surfaceof theearth. Whatwould be
its weightwhen measured on the surface of the moon?
29. Example-3 A stone is allowed to fall from the top of a tower 100 m high and at the same time
another stone is projected vertically upwards from the ground with a velocity of 25 m/s.
Calculate when and where the two stones will meet.
30.
31. Motion of objects under the influence of
Gravitational force of the Earth
Activity 10.3
• Take a sheetof paperand a stone. Drop them
simultaneously from the first floor of a building. Observe
whether both of them reach theground simultaneously.
• We see that paperreaches theground little later than the
stone. This happens becauseof airresistance. Theairoffers
resistance due to friction to the motion of the falling
objects. The resistance offered by air to the paper is more
than the resistance offered to the stone. If we do the
experiment in a glass jar from which air has been sucked
out, the paperand the stone would fall at the same rate.
32. Mass of an object is 10 kg. What is its weight on the earth? An
object weighs 10 N when measured on the surface of the earth.
Whatwould be itsweightwhen measured on the surfaceof the
moon?
Why is the weight of an object on the moon 1/6 th its weight on
the earth?
How does thevalue of g changes form pole toequator?
What is SI unitof Gravitation force?
Give the standard valueof accelerationdue togravity(g)onearth
surface.
A stone is thrown verticallyupward with an initial velocity of
40 m/s. Taking g = 10 m s–2, find the maximum height reached
by the stone. What is the netdisplacementand the total
distancecovered by the stone?
