# Our Universe: GRAVITATION

From Ancient times many scientists had shown great interest towards the sky. Most of

the scientist studied the motion of celestial bodies.

One of the most influential greek astronomers and geographers of his time, "Ptolemy"

propounded the geocentric theory in a form that prevailed for 1400 years. He made

astronomical observations from Alexandria in Egypt during the year. AD 127-41. Infact the

first observation which can date exactly was made by Ptolemy on 26 march 127. While last

was made on 2nd feb 141.

The Almagest is the earliest of ptolemy work and gives in detail the mathematical theory

of motions. Of sun, moon and planets. Ptolemy made his most original contribution by

presenting details for the motion of each of the planets. The almagest was not super seeded

until a century after copernicus presented his heliocentric theory.

Ptolemy first of all justifies his descriptions of the universe based on earth - centred

system. It is a view of the world based on fixed earth around which the sphere of the fixed

stars rotates every day, this carrying with it the sphere of the sun, moon and planets.

**Nicolas Copernicus:**

In 16th century AD nicolas copernicus, a polish monk was born on 19th feb 1473 and the died

on may 24, 1543

Copernicus summerised his heliocentric theory. According to this theory, the earth and

other planets moved in perfect circles around the sun located at the centre of these circles.

The earth and other planets would also rotate about their own axes while orbiting around the

sum in circular orbits of different radii.

Johannes Kepler (1571-1630) was a German mathematician, astronomer and astrologer

and key figure in the 17th century scientific revolution. He was assistant to astronomer Tycho

Brache. He learned both the ptolemic system and copernican system of planetary motion.

He believed copernicas at that time. He defended heliocentrism form both theoretical and

theological perspective, maintaining that the sun was the principal source of motive power

in the Universe.

**Issac Newton:**

The English physicist issac newton (1642-1727) introduced the term "Gravity" after he saw

an apple falling on to the ground in his garden. "Gravity" is the force of attraction exerted by

the earth on an object. The moon orbits around the earth because of gravity too. Newton

later proposed that gravity too. Newton later proposed that gravity was fast a particular case

of gravitation. Every mass in the universe attracts every other mass. This is the idea of

Newton's law of Gravitation.

Newton derived the relation in such a way that F is proportional to 'm'. because the force

on a body is directly proportional to its mass by Newton's 2nd law of motion F=ma. When

the earth exerts a force on the falling body, by the Newton's 3rd law of motion. The falling

body exerts an equal and opposite force on the earth. Therefore the gravitational force F is

proportion to both the masses of falling body and the earth, i.e., m1 and m2. The inverse

square relationship 1/r

2, was justified by observing motion of the moon.

Newton also observed that it is not only the earth which attracts other objects, but every

object in the universe attracts every other objects and he termed such a general force as

''gravitational force". One law is known as the Universal law of gravitation".

According to this law, the gravitational force of attraction between any two objects is

i) Directly proportional to the product of their masses.

ii) Inversely proportional to the square of the distance between them.

If the masses of any two objects are 'm1' and m2 and the separation between them is r

then the gravitation at force of attraction between them is

Where 'G' is proportionality constant and known as ''Universal Gravitational Constant".

"Every body in the Universe attracts every other body with a force which is directly

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

distance between them. The force acts along the line joining the two bodies"

The Universal Gravitational Constant 'G':

We know that or

Units of G:

- In SI system units of 'F' is Newton (N)

- Units of Distance (r) is meter (m)

- Units of mass (m) is kilogram (kg)

The numerical value of 'G' is experimentally found to be 6.67 × 10–11Nm2Kg –2

**Acceleration due to gravity:**

Galileo proved, (from leaning tower of pisa experiment) that objects of different masses

and sizes, when dropped simultaneously from the same height, would reach the ground at

same time.

In other words when an object is dropped from some height, it experiences uniform

acceleration by the gravitational pull of the earth and this acceleration does not depend on

the mass of the body.

The uniform acceleration produced in a freely falling body due to the gravitational pull of

the earth is known as acceleration due to gravity and denoted by letter 'g' is given by the

equation g = GM/r2.............. (5)

where G =Universal Gravitational Constant (6.67 × 10–11Nm2/kg2)

M =Mass of the Earth( 6 × 1024kg)

r =Radius of Earth(6.4 × 106m)

from the equation (5) Value of g is g = 9.8 ms–2

**Variation of 'g' value:**At a given place on the earth 'g' is constant. However, it varies due

to the fact that the earth is not a perfect sphere and its radius 'r' is not the same at all places

on its surface. Due to flattering of the earth at the poles, 'r' is minimum and hence 'g' is

maximum at the poles. Since 'r' is maximum at the equator, the value of 'g' becomes

minimum at the equator. The value of 'g' decreases as we move upwards from the surface.

As we go deep in to the earth (mine), the value of 'g' decreases.

**Gravity meters:**The instrument used to measure small changes in the value of 'g' at a given

location is known as gravity meters. The Boldien gravity meter and Gulf gravity meters are

two examples of gravity meter.

**Mass and weight**: The mass of a body is the quantity of matter contained in it. Mass is

independent of external factors like position and surroundings. Thus the mass of a given

body will be same at all place of earth or any where in the University.

The weight of a body is the force with which it is attracted by the earth towards its centre

and is equal to the product of its mass and acceleration due to gravity.

Thus w = mg, where 'm' is mass of body and 'g' is the acceleration due to gravity.

Since the value of 'g' changes from place to place, the weight of a given body differs from

one place to another. For example: The acceleration due to gravity on moon is 1/6th of the

acceleration due to gravity on earth, hence the weight of the body on moon is 1/6th of its

weight on earth.

**Very Short Answer Questions (1 Mark)**

**1. What is Geocentric theory?**

A- The earth is stationary and is at the centre of the universe, with the sun, the moon,

planets and stars revolving the earth.

**2. What is Heliocentric theory?**

A- All the planets revolve in a perfect circle with the stationary sun at the centre of these

circles.

**3. What is acceleration due to gravity?**

A- 1.The Uniform acceleration produced in a freely falling body due to gravitational pull of

the earth is called acceleration due to gravity.

2. It is denoted by (g)

**4. Define the mass of a body?**

A- The total quantity of matter contained in a body is defined as its mass.

**5. Define the weight of a body.**

A- The weight of a body is the force with which it is pulled by the earth towards its centre.

**6. State Hooke's law?**

A- According to Hooke's law "Stress is directly proportional to strain when a body is in

elastic limit''

**7. Calculate the gravitational force on a stone of mass 10kg?**

A- Acceleration due to gravity (g) = 9.8m/sec2

mass of the stone, m=10kg

The gravitational force on the stone,

F = mg = 10 × 9.8 = 98 newton.

**8. Define 1 kg wt?**

A- The gravitational force acting on a body of mass 1kg is called 1kg wt.

**9. What is the relation between 'g' and 'G'?**

A- g=GM/r2

**SHORT ANSWER QUESTION (2M)**

**1. State the Universal law of gravitation? and calculate the gravitational force of**

**stone of mass. 10kg.**

A- Newton's Universal law of gravitation states ''that every body in the universe attracts

every other body with a force which is directly proportional to the product of their masses

and inversely proportional to the square of the distance between them"

Problem: We know that F = mg

= F = 10 × 9.8 = 98 N

**2. What are the various factors that effect on the value of acceleration due to gravity**

**(g)?**

A- The various factors that influence the value of 'g' are

1. Shape of the earth

a) At poles

b) At equator

2. Height (Altitude)

3. Depth

4. Local Conditions

**3. Why is the weight of a body not the same at poles and equator?**

A- The weight of a body W=mg. So it depends on acceleration due to gravity. It is directly

proportional to acceleration due to gravity. As the acceleration due to gravity is not same

at the poles and equator, the weight of a body is also not the same at the poles and the

equator.

**4. Why does the weight of a body differs from one place to another place?**

A- The weight of a body w=mg. It means the weight of a body is directly proportional

acceleration due to gravity. As the value of acceleration due to gravity 'g' changes from

place to place, the weight of a body also changes from place to place.

**5. What is gravity meter? Give examples?**

1. The value of g at a given location is slightly affected by geological deposits

concentration of massive concrete building and topography of the region

2. So,a sensitive instrument is used to measure such small changes in the value of g at a

given location.

3. This instrument is called gravity meter.

4. Examples: Gulf gravity meter and Boliden gravity meter.

**6. Differential between mass and weight of a body.**

- The following are the differences between mass and weight.

**Essay Type Questions**

**1. Write Newton's law of universal Gravitation and derive F=m1m2/r2.**

A. Newton's law of universal Gravitation: Everybody in the universe attracts every other

body with a force which is directly proportional to the product of their masses and

inversely proportional to the square of the distance between them. The force acts along

the line joining the two bodies.

Let the masses of any two bodies be m1 and m2 and they are separated by distance ''r''.

The gravitational force of attraction between the two bodies is directly proportional to

the product of their masses.

F - m1m2.................(1)

The Gravitational force of attraction between the bodies is inversely proportional to the

square of the distance between them.

F a 1/r2 .................. (2)

From (1) and (2)

Where G is the proportionality constant and is called ''Universal Gravitational Constant"

**2. Explain the change in the value of 'g' as we go from the surface of the earth to deep**

**inside?**

1. 'g' value decreases from the surface of the Earth to deep inside.

2. The reason for the decreases in 'g' value is decrease of effective mass of the Earth.

3. The effective mass of the earth is given by the equation Where p is the average density of the Earth.

4. From the above equation, the effective mass M influencing the body decreases inside the

mine as effective r decreases.

5. If g is acceleration due to gravity at a depth ''d'' inside the mine and g is acceleration due

to gravity on the surface, then the relation between them is given by

6. Thus at the centre of the earth (d=r) so"gd'' value becomes zero at center of earth.

**3. Derive the relation between acceleration due to gravity and Gravitational**

**constant?**

- Let 'G' and 'g' be universal Gravitational constant and acceleration due to gravity.

Suppose a stone of mass 'm' is dropped from a distance 'r' from the centre of the Earth

of mass M, then the force exerted by the Earth on the stone is given by the Universal law

of Gravitation as.

F= G Mm/r2 .........(1)

This force produces acceleration 'g' on the stone but according to Newton's second law

of motion.

F = mg ............(2)

mg=G Mm/r2

Hence g=G M/r2

from the above equation, g is independent of the value of the mass of the stone.

**4. Describe an experiment to determine the weight of a body?**

**Aim:**To determine the weight of a body.

**Apparatus: A**n extensible spring, pan, weights, stand, metre scale, plasticine.

**Method:**Suspend the spring to the stand. Attach a pan to the lower end of the spring.

Also fix a pin at the lower end of the spring. Also fix a pin at the lower end of the spring

at right angles to the spring by means of a little plasticine.

The horizontal pin serves as a pointer. Fix the metre scale vertically so that the pointer Can more over the scale.

Record the reading of the pointer on the scale (lo) initially. Add a 10 gram weight of the scale pan. Note the reading of the pointer (l1). Record the readings by adding 10 gramseach time.

Plot a graph between stretching ((l – l0) against force (F). This graph is a straight and is called Calibration graph for the spring.

Force Balance Readings (m) Mean Length Extension of the spring (gm.wt) Loading Unloading l (cm) (l – l0)

Now place the body on the pan and note down the extension (l-lo).

Locate the point of (l-lo) On Y-axis And Read The Corresponding X-ordinate. This gives the weight of the body.

**Multiple Choice Questions**

a) Circular Orbit

b) Elliptical Orbit

c) Rectangular Orbit

d) Linear

2. The law of Gravitation ( )

a) applies only to large bodies such as planets and stars

b) accounts for all known forces

c) holds only in the solar system

d) holds everywhere in the universe.

3. The weight of 400g stone is ( )

a) 0.041

b) 0.4N

c) 3.92 N

d) 3920 N

4. The distance of the Moon and from the Earth is about? ( )

a) 3.85 × 105 km

b) 3.85 × 105 m

c) 385 × 105 km

d) 385 × 105 m

5. The Unit of force in S.I. system is ( )

a) metre

b) Pascal

c) Newton

d) Newton Metre

6. The units of gravitational constant ( )

a) Nm2kg–2

b) Nmkg – 2

c) Nm2kg2

d) Nm–2 kg–2

7. The Gravitational force of attraction between any two bodies is ( )

8. All bodies large or small falls on the ground with the same ( )

a) Force

b) Velocity

c) acceleration

d) momentum

9. As we go from the equator to the poles, the values of 'g' ( )

a) remains the same

b) decreases

c) increases

d) decreases up to altitude of 45°

10. Value of 'g' on the Earth is ( )

a) 9.8 ms–2

b) 1.67 ms–2

c) 98 ms–2

d) 167 ms–2

11.The relation between g and G is ( )

a) G = 9

b) g = GM/r2

c) g = Gr2

d) None of these

12.Acceleration due to gravity at a height 'h' from the surface of the Earth is ( )

13.Which of the following instrument used to measure small changes in the value of 'g'? ( )

a) Boliden Gravity Meter

b) Ammeter

c) Voltmeter

d) Galvanometer

14.1kg Weight = ( )

a) 9.8 ergs

b) 9.8 joule

c) 9.8 kg

d) 9.8 newton

15.Which one of the following is changes with change in place? ( )

a) mass

b) weight

c) mass and weight

d) None

**II. Fill in the blanks**

1. Ptolemic theory is also known as _______

2. Copernicas theory is known as ________

3. The weight of 500g stone is _______ N

4. Units of Universal Gravitational constant G are _____

5. Units of acceleration due to gravity are ______

6. Acceleration due to gravity is independent of _______

7. Acceleration due to gravity maximum at earth's______ the and minimum at the ______

8. Mass of a body is ______ any where in the Universe.

9. Mass of a body changes from _____ to place.

10.The distance of the moon from the earth is about ______

11.According to Newton's second law of Motion F = mass × ______

12.Acceleration due to gravity is independent of the value of the _____ of the stone.

13.Acceleration due to gravity at the centre of the Earth _____

14.____ law helps in the determination of the weight of the body.

15.The 'g' value of sun is _____

16.The weight of the body is the ______ of the earth's gravity acting on it.

17.In formula2 G stands for ______

III. Match the following

**Answers.**

1. a

2. d

3. c

4. a

5. c

6. a

7. c

8. c

9. c

10. a

11. b

12. a

13. a

14. d

15. b

**Fill in the blanks**

1. Geocentric Theory

2. Heliocentric Theory

3. 4.9

4. Nm2Kg–2

5. ms–2

6. mass of the bodies

7. poles, equator

8. same

9. place10. 3.85 × 105km

11. acceleration

12. mass

13. zero

14. Hooke's Law

15. 27.4ms-2

16. Force of attraction

17. Universal Gravitational Constant

**Match the following**

1. d

2. f

3. h

4. a

5. c

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