## Gravitation notes

Gravitation :

Gravitation is the force of attraction between two objects in the universe.

i) Gravitation may be the attraction of objects by the earth. Eg :- If a body is dropped from a

certain height, it falls downwards due to earth’s gravity.If a body is thrown upwards, it reaches a certain height and then falls downwards due to the earth’s gravity.

ii) Gravitation may be the attraction between objects in outer space.

Eg :- Attraction between the earth and moon. Attraction between the sun and planets.

Centripetal force :-

When a body moves in a circular path, it changes its direction at every point. The force which keeps the body in the circular path acts towards the centre of the circle. This force is called centripetal force.

If there is no centripetal force, the body will move in a straight line tangent to the circular path.

2) Universal law of gravitation :-

The universal law of gravitation states that, ‘Every object in the universe attracts every other

object with a force which is directly proportional to product of the masses and inversely

proportional to the square of the distance between them.’

Let two objects A and B of masses M and m lie at a distance d from each other. Let F be the

force of attraction between them.According to the universal law of gravitation the force between the objects is directly

proportional to the product of their masses and inversely proportional to the square of the

distance between them

F α M x m

and F α 1/ d2W . J N I L T Combining the two equations F α Mxm/ d2

Or F = G Mxm/ d2

where G is a constant of proportionality called universal gravitation constant

Cross multiplying we get

F x d2 = G M x m or G = F x d2/ M x m

The SI unit of G is N m2 kg -2 and its value is 6.673 x 10-11 N m2 kg -2

3) Free fall :- The earth attracts objects towards it due to gravitational force. When an object

falls towards the earth due to the earth’s gravitational force it is called free fall.

When an object falls towards the earth there is a change in its acceleration due to the

gravitational force of the earth. So this acceleration is called acceleration due to gravity.

The acceleration due to gravity is denoted by g.

The unit of g is same as the unit of acceleration ms -2

From the second law of motion, force is the product of mass and acceleration.

F = ma

For free fall, force is the product of mass and acceleration due to gravity.

F = mg

g = G m/d2

where M is the mass of the earth and d is the distance between the object and the earth.

For objects near or on the surface of the earth d is equal to the radius of the earth R

mg = G M x m/ R2 or g = G M/ R2 The value of g is 9.8 ms -2

4 a) Mass :- The mass of a body is the measure of its inertia. If the mass of a body is more its inertia is more. The mass of a body is constant and does not change from place to place.

The SI unit of mass is kg.

b) Weight :- The weight of a body is the force with which the earth attracts the body.

The force with which a body is attracted by the earth depends on its mass

*m*and acceleration
due to gravity

*g.**F = m x g*

Since weight of a body is the force with which the earth attracts the body,

*W = m x g*

Since

*g*at a place is constant ,*W**α**m*
The weight of a body changes from place to place.

The SI unit of weight is the same as force – Newton (N).

c) Weight of an object on the moon :- The weight of an object on the earth is the force with

which the earth attracts the object and the weight of an object on the moon is the force with

which the moon attracts the object.

The mass of the moon is less than the mass of the earth. So the moon exerts lesser force on the objects than the earth.

The weight of an object on the moon is one sixth (1/6th) of its weight on the earth.

5) Thrust and pressure :-

a) Thrust :- Thrust is the force acting on an object perpendicular to the surface. Eg :- When

you stand on loose sand the force (weight) of your body is acting on an area equal to the area of your feet. When you lie down, the same force acts on an area equal to the contact area of the whole body. In both cases the force acting on the sand (thrust) is the same.

b) Pressure :- Pressure is the force acting on unit area of a surface.

W W W . J S U N I L T U T O R Pressure = Thrust/ Area

Eg :- The effect of thrust on loose sand is larger while standing than while lying down.

The SI unit of thrust is N/m2 or N m-2 . It is called Pascal (Pa).

6 a) Pressure in fluids (Liquids and gases) :- Fluids exert pressure on the base and walls of the container. Fluids exert pressure in all directions. Pressure exerted on fluids is transmitted equally in all directions.

b) Buoyancy (Upthrust) :-

When an object is immersed in a fluid it experiences an upward force called buoyant force.

This property is called buoyancy or upthrust. The force of gravity pulls the object downward

and the buoyant force pushes it upwards. The magnitude of the buoyant force depends upon the density of the fluid.

c) Why objects float or sink in water ?

If the density of an object is less than the density of a liquid, it will float on the liquid and if the density of an object is more than the density of a liquid, it will sink in the liquid.

Activity :-

Take some water in a beaker. Take a piece of cork and an iron nail of the same mass. Place

them on the water. The cork floats and the nail sinks.

The cork floats because the density of cork is less than the density of water and the upthrust

of water is more than the weight of the cork.

The nail sinks because the density of the iron nail is more than the density of water and the

upthrust of water is less than the weight of the nail.

7) Archimedes’ principle :-

Archimedes’ principle states that, ‘ When a body is partially or fully immersed in a fluid it

experiences an upward force that is equal to the weight of the fluid displaced by it.’W . J S U N I L Archimedes principle has many uses. It is used in designing ships and submarines,

Hydrometers used to determine the density of liquids, lactometers used to determine purity of milk etc.

8) Density and relative density :-

i) Density :- The density of a substance is the mass of a unit volume of the substance.

Density = Mass/ Volume

The unit of density is kilogram per metre cube (kg m -3).

ii) Relative density :- The relative density of a substance is the ratio of the density of a

substance to the density of water.

Relative density = Density of a substance/ Density of water

Since relative density is a ratio of similar quantities, it has no unit.

**TEST PAPER-**

1. If cross – sectional area of an object is more than the pressure applied by the

external force is :-

(a) Less (b) More (c) Remains same (d) None of the above.[1]

2. If the acceleration due to gravity at a place is more, the weight of that object will :-

(a) Decrease (b) Increase (c) Remains same (d) None of the above[1]

3. Weight of the object is:-

(a) More at the equator and less at poles (b) More at poles and less at equator

(d) Same at poles and equator (d) Depend on Mass of the object[1]

4. If the distance between the object increase, mass remaining same then the

gravitational forces between the object will :-

(a) Increase (b) Decrease (c) Remain same (d) None of the above.[1]

5. How does acceleration due to gravity change with the shape of earth?[2]

6. What do you understand by the gravitational force of earth and weight?[2]

7. A man of mass 60 Kg is standing on the floor holding a stone weighing 40N. What is

the force with which the floor is pushing him up?[2]

8. What is acceleration due to gravity and how is it different from acceleration?[2]

9. What is acceleration due to gravity and calculate its value on earth?[3]

10. A ball is thrown vertically upwards. The speed of the ball was 10m/s when it had

reached one half of its maximum height.

(a) How high does the ball rise?

(b) Find the velocity and acceleration 1s after it is thrown.[3]

11. How does weight of a rocket change as it moves from earth to moon?[3]

12. Give a mathematical proof of the Archimedes principle? [3]

13. The Olympic high jump record is 2.45m held by Cuba let acceleration due to gravity

on earth was – 1m/s2 and not -10m/s2. Calculate the height to which the jumper

would have jumped?[5]

**TEST PAPER-**

1. Units of pressure are :- (a) N/m2 (b) m2/N (c) Nm2 (d) Nm[1]

2. Units of Relative Density are :-

(a) Kg/m3 (c) Depends on the density of the substance

(b) Unit less (d) Depend on the density of water [1]

3. Pressure at a point in the liquid is

(a) Same in all directions (b) Greater in the upward direction

(c) Grater in the downward direction (d) None of the Above [1]

4. If the area of an object is less then the pressure acting on that object will be

(a) Less (b) More (c) Independent of area (d) None of the above [1]

5. Define Pressure? How is thrust different from Pressure?[2]

6. What are fluids? What are the factors on which the upward pressure at a point on

a fluid depends?[2]

7. Define density and relative density?[2]

8. Calculate the pressure at a depth of 50m below the surface of sea. The density of

sea water is 1024 Kg/m3.[2]

9. What makes a body to float or sink in a liquid?[3]

10. A block of wood tied to the bottom of

water tank as shown. The wooden block

exerts tension, on the wire tied to it. The

dimension of the block are 20cm × 20cm

× 40cm.

The density of the wood is 600Kg/m3.

What is the tension in the wire?[3]

11. The weight of balloon and gas inside it is 12KN. The volume of the balloon is

1200m3. The density of air is 1.26 Kg/m3. Calculate

a) the weight it can lift

b) the acceleration as it rises.[3]

12. A cylindrical block of wood of height 4.2m and mass 100Kg floats vertically in

water. The relative density of wood is 0.8

**Read more topics**

http://www.scc-education.com/2015/06/1.html

) Gravitation :

Gravitation is that the force of attraction between 2 objects within the universe.

i) Gravitation is also the attraction of objects by the planet. Eg :- If a body is born from a

certain height, it falls downward as a result of earth’s gravity.If a body is thrown upwards, it reaches a precise heightthen falls downward as a result of the earth’s gravity.

ii) Gravitation is also the attraction between objects in space.

Eg :- Attraction between the planet and moon. Attraction between the sun and planets.

Centripetal force :-

When a body moves during a circular path, it changes its direction at each purpose. The force that

keeps the body within the circular path acts towards the centre of the circle. This force is named

centripetal force.

If there's no force, the body can move during a line tangent to the circular path.

2) Universal law of gravitation :-

The universal law of gravitation states that, ‘Every object within the universe attracts each different

object with a force that is directly proportional to product of the plenty and reciprocally

proportional to the sq. of the gap between them.’

Let 2 objects A and B of plenty M and m lie at a distance d from one another. Let F be the

force of attraction between them.

According to the universal law of gravitation the force between the objects is directly

proportional to the merchandise of their plenty and reciprocally proportional to the sq. of the

distance between them

F α M x m

and F α 1/ d2W . J N I L T Combining the 2 equations F α Mxm/ d2

Or F = G Mxm/ d2

where G could be a constant of proportion referred to as universal gravitation constant

Cross multiplying we tend to get

F x d2 = G M x m or G = F x d2/ M x m

The SI unit of G is N M2 weight unit -2 and its price is vi.673 x 10-11 N M2 weight unit -2

3) Free fall :- the planet attracts objects towards it as a result of gravity. once AN object

falls towards the planet as a result of the earth’s gravity it's referred to as free fall.

When AN object falls towards the planet there's a modification in its acceleration as a result of the

gravitational force of the planet. therefore this acceleration is named acceleration as a result of gravity.

The acceleration as a result of gravity is denoted by g.

The unit of g is same because the unit of acceleration ms -2

From the second law of motion, force is that the product of mass and acceleration.

F = ma

For free fall, force is that the product of mass and acceleration as a result of gravity.

F = mg

) Gravitation :

Gravitation is that the force of attraction between 2 objects within the universe.

i) Gravitation is also the attraction of objects by the planet. Eg :- If a body is born from a

certain height, it falls downward as a result of earth’s gravity.If a body is thrown upwards, it reaches a precise heightthen falls downward as a result of the earth’s gravity.

ii) Gravitation is also the attraction between objects in space.

Eg :- Attraction between the planet and moon. Attraction between the sun and planets.

Centripetal force :-

When a body moves during a circular path, it changes its direction at each purpose. The force that

keeps the body within the circular path acts towards the centre of the circle. This force is named

centripetal force.

If there's no force, the body can move during a line tangent to the circular path.

2) Universal law of gravitation :-

The universal law of gravitation states that, ‘Every object within the universe attracts each different

object with a force that is directly proportional to product of the plenty and reciprocally

proportional to the sq. of the gap between them.’

Let 2 objects A and B of plenty M and m lie at a distance d from one another. Let F be the

force of attraction between them.

According to the universal law of gravitation the force between the objects is directly

proportional to the merchandise of their plenty and reciprocally proportional to the sq. of the

distance between them

F α M x m

and F α 1/ d2W . J N I L T Combining the 2 equations F α Mxm/ d2

Or F = G Mxm/ d2

where G could be a constant of proportion referred to as universal gravitation constant

Cross multiplying we tend to get

F x d2 = G M x m or G = F x d2/ M x m

The SI unit of G is N M2 weight unit -2 and its price is vi.673 x 10-11 N M2 weight unit -2

3) Free fall :- the planet attracts objects towards it as a result of gravity. once AN object

falls towards the planet as a result of the earth’s gravity it's referred to as free fall.

When AN object falls towards the planet there's a modification in its acceleration as a result of the

gravitational force of the planet. therefore this acceleration is named acceleration as a result of gravity.

The acceleration as a result of gravity is denoted by g.

The unit of g is same because the unit of acceleration ms -2

From the second law of motion, force is that the product of mass and acceleration.

F = ma

For free fall, force is that the product of mass and acceleration as a result of gravity.

F = mg

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