Gravitation

Centripetal Force

 Definition - The force that causes this acceleration and keeps the body moving along the circular
path is acting towards the centre. This force is called the centripetal (meaning ‘centre-seeking’)
force.
 In the absence of this force, the stone flies off along a straight line. This straight line will be a
tangent to the circular path.
 Example - The motion of the moon around the earth is due to the centripetal force. If there
were no such force, the moon would pursue a uniform straight-line motion.

Gravitational Force

 Definition -This force of attraction between objects is called the gravitational force.
 Gravitation is a weak force unless large masses are involved.
 The force of gravity decreases with altitude. It also varies on the surface of the earth, decreasing
from poles to the equator.
 The SI unit of G - N m2 kg–2
 Found the value of G - Henry Cavendish
 Value of G - 6.673 × 10–11 N m2 kg–2
 The law of gravitation states that the force of attraction between any two objects is
proportional to the product of their masses and inversely proportional to the square of the
distance between them. The law applies to objects anywhere in the universe. Such a law is said
to be universal.
 Importance of the universal law of gravitation
o The force that binds us to the earth
o The motion of the moon around the earth
o The motion of planets around the Sun
o The tides due to the moon and the Sun.
 Derivation of Universal Law of Gravitation

Free Fall

 Definition - The earth attracts objects towards it. This is due to the gravitational force.
Whenever objects fall towards the earth under this force alone, we say that the objects are in
free fall.
 Definition of acceleration due to gravity - Whenever an object falls towards the earth, an
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
 Unit of acceleration due to gravity - g (ms-2)
 Derivation of acceleration due to gravity
 The value of acceleration due to gravity of the earth is g = 9.8 m s-2.
Mass

 The mass of an object is constant and does not change from place to place

Weight

 The force of attraction of the earth on an object is known as the weight of the object.
 The weight is equal to the product of mass and acceleration due to gravity
 Derivation of weight of object on moon

Thrust and Pressure

 Thrust Definition - The force acting on an object perpendicular to the surface is called thrust.
 The effect of thrust depends on the area on which it acts - The same force acting on a smaller
area exerts a larger pressure, and a smaller pressure on a larger area.
 Pressure Definition - The thrust on unit area is called pressure.
 SI unit of thrust is N
 SI unit of pressure as N/m2 or Pa
 This is the reason why a nail has a pointed tip; knives have sharp edges; buildings have wide
foundations; a camel can run in a desert easily; an army tank weighing more than a thousand
tonne rests upon a continuous chain; a truck or a motorbus has much wider tyres. (as pressure is
force per unit area…distributes weight over a large area…reduction of pressure)
 Pressure in fluids:
o All liquids and gases are fluids. A solid exerts pressure on a surface due to its weight.
o Similarly, fluids have weight, and they also exert pressure on the base and walls of the
container in which they are enclosed.
o Pressure exerted in any confined mass of fluid is transmitted undiminished in all
directions.

Buoyancy

 Definition: The upward force exerted by the water on the bottle is known as upthrust or
buoyant force. All objects experience a force of buoyancy when they are immersed in a fluid.
 The magnitude of this buoyant force depends on the density of the fluid.
 Examples: Had a swim in a pool and felt lighter; drawn water from a well and felt that the
bucket of water is heavier when it is out of the water; A ship made of iron and steel does not
sink in sea water, but while the same amount of iron and steel in the form of a sheet would sink.
(weight due to force of gravitational attraction acts downward…water exerts force in upward
direction…makes us feel lighter), (A ship is a hollow object made of iron and steel which contains
a lot of air in it…air density low)
 Sink or float:

 Why do objects sink or float? The force due to the gravitational attraction of the earth on the
object pulls it downwards. While the Buoyant force of water on the object pushes it upwards.
This causes an object to sink or float
 Definition of Density - The density of a substance is defined as the mass per unit volume.
 Objects of density less than that of a liquid float on the liquid. The objects of density greater
than that of a liquid sink in the liquid.

Archimedes’ Principle

 When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal
to the weight of the fluid displaced by it.
 Applications of Archimedes’ Principle
o It is used in designing ships and submarines. Lactometers, which are used to determine
the purity of a sample of milk and hydrometers used for determining density of liquids,
are based on this principle.

Questions

1. How does the force of gravitation between two objects change when the distance between
them is reduced to half?
2. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object
does not fall faster than a light object?
3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its
surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m.)
4. 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?
5. If the moon attracts the earth, why does the earth not move towards the moon?
6. What happens to the force between two objects, if
(i) the mass of one object is doubled?
(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?
7. What is the importance of universal law of gravitation?
8. What is the acceleration of free fall?
9. What do we call the gravitational force between the earth and an object?
10. Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands
over the same when he meets him at the equator. Will the friend agree with the weight of gold
bought? If not, why? [Hint: The value of g is greater at the poles than at the equator.]
11. Why will a sheet of paper fall slower than one that is crumpled into a ball?
12. Gravitational force on the surface of the moon is only 1/6 as strong as gravitational force on the
earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises
(ii) the total time it takes to return to the surface of the earth.
14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just
before touching the ground.
15. A stone is thrown vertically upward 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 net displacement and the total distance
covered by the stone?
16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the
earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 ×
1011 m.
17. 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.
18. A ball thrown up vertically returns to the thrower after 6 s. Find (a) the velocity with which it
was thrown up, (b) the maximum height it reaches, and (c) its position after 4 s.
19. In what direction does the buoyant force on an object immersed in a liquid act?
20. Why does a block of plastic released under water come up to the surface of water?
21. The volume of 50 g of a substance is 20 cm3. If the density of water is 1 g cm–3, will the
substance float or sink?
22. The volume of a 500 g sealed packet is 350 cm3. Will the packet float or sink in water if the
density of water is 1 g cm–3? What will be the mass of the water displaced by this packet?
23. The mass of the earth is 6 × 1024 kg and that of the moon is 7.4 × 1022 kg. If the distance between
the earth and the moon is 3.84×105 km, calculate the force exerted by the earth on the moon.
(Take G = 6.7 × 10–11 N m2 kg-2)
24. A car falls off a ledge and drops to the ground in 0.5 s. Let g = 10 m s–2
(i) What is its speed on striking the ground?
(ii) What is its average speed during the 0.5 s?
(iii) How high is the ledge from the ground?
25. An object is thrown vertically upwards and rises to a height of 10 m. Calculate
(i) The velocity with which the object was thrown upwards
(ii) The time taken by the object to reach the highest point.
26. Mass of an object is 10 kg. What is its weight on the earth?
27. An object weighs 10 N when measured on the surface of the earth. What would be its weight
when measured on the surface of the moon?
28. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
29. You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a
weighing machine. In reality, one is heavier than other. Can you say which one is heavier and
why?