# Force lesson note-Science (Preparation for SEE)

# Force

It is defined as a push or pull that change or tends to change the state of rest or of uniform motion of a body along a straight line.

# Newton’s Universal law of gravitation

“Everybody in this universe attracts every another body with a force which is (i) directly proportional to the product of their masses and (ii) inversely proportional to the square of the distance between their centers”.

Consider a body of mass m1 attracts another body of mass m2 with a force F towards its centre O1. The body of mass m2 in turn attracts the body of mass m1 with the same force F towards its centre O2. Suppose the distance between their centers is‘d’ then, according to Newton’s universal law of gravitation, we have

F ∞ m1 x m2 … (i)

And F ∞ … (ii)

Combining these two equations (I) and (ii), we have

F ∞

Or, F = G …………. (iii)

Where G is called a proportionally constant or universal gravitational constant. The value of The G is determined form experiment.

Hence, the equation (iii) gives the measure of the gravitational force between two masses.

# Universal gravitational constant ‘G’

Universal gravitational constant ‘G’ can be defined as the force of gravitation that is exerted between two unit masses, separated from one another by a unit distance.

The SI unit of G is Nm2kg-2.

The approximate value of G is 6.67 10-11Nm2kg-2.

# Properties of G

The value of G is independent of the nature and chemical composition of the masses of the bodies, and the medium in which the bodies are occurred.

The value of G is unaffected by temperature and pressure.

# Consequences of gravitational force

The presence of solar system and planets revolve round the sun due to the presence of gravitational force.

The presence of atmosphere on the earth is due to the gravitational force.

The gravitational force of the earth keeps us firmly on the surface of the earth.

Tides in seas and oceans are due to the gravitational force of the sun and moon.

# Special features of gravitational force

The gravitational forces between two bodies constitute on action and reaction pair.

The gravitational force between two bodies does not depend upon the nature of the intervening medium.

The gravitational force between light bodies is extremely small and hence such smaller force is not felt in practice. However, it becomes appreciable in case of massive bodies.

# Gravity or weight

The force of attraction of the earth on a body is called force of gravity or simply the weight of the body on earth.

Let a body of mass m be placed on the surface of the earth of mass M as shown in the figure. The distance between them can be taken to be equal to the radius (R) of the earth. The weight (W) of the body on the surface of the earth is given by,

W = G …………….. (i) (

If m is kept constant,

W∞ ……….. (ii)

Equation (ii) shows that weight (W) of a body on the surface of a planet/ satellite is directly proportional to mass (M) of the planet /satellite. Greater the mass of the planet /satellite, larger its gravity is i.e., greater will be the weight of the body on the planet/satellite.

Equation (ii) also shows that weight (W) of a body on the surface of a planet/satellite is inversely proportional to the square of the radius (R) of the planet/satellite. The weight of the body will be less if it becomes large.

# Effects of gravity

We are able to stand up, run and perform other activities freely due to gravity of the earth.

Construction of building and bridges is possible due to the gravity of the earth.

There will be no atmosphere around the earth in the absence of gravity of the earth.

If a body is thrown upwards, its notion is opposed by gravity of the earth. So, it falls back to the earth.

Tides occur by the gravity of the moon on ocean water.

# Acceleration due to gravity

Acceleration due to gravity is defined as the acceleration produced in a freely falling body due to the force of gravity of the earth towards its center. It is denoted by g and its average value is 9.8 m/s2.

# Relation between Radius and Gravity

Let M be the mass of the earth and R its radius, then the force of attraction on a body of mass m on its surface as given by the Newton’s Universal law of gravitation is

But, the force with which the body is attracted towards the center of the earth is the weight of the body.

As (i) and (ii) represents the same force, we get,

This is the expression for the acceleration due to gravity. The value of g on the surface of the earth is

Independent of mass of the body

Depends on the mass of the earth and the radius

iii. Suggests that the value of g at a particular place is constant.

# Variation in the value of g

Variation due to shape [ On the surface]

Variation with height

Variation with depth

…………………(c)

# Gravitational field and Gravitational field intensity

The space around a mass over which it can exert gravitational force on other masses is called the gravitational field of the mass.

The gravitational field intensity at a point in the gravitational field is defined as the force experienced by unit mass placed at that point. Its unit is N/Kg.

Gravitational field intensity I and acceleration due to gravity g are one and the same thing, so

# Mass

The amount of substance contained in a body is called the mass. The mass of the body is measured by using a physical balance or beam balance. It unit if kg in SI. The mass of the body is dependent upon the number of atoms and average mass of atoms present in the body.

# Weight

The weight of a body is defined as the force with which it is attracted towards the center of the earth. SI unit of weight is Newton (N). Its value changes from place to place as it depends on the acceleration due to gravity (g). It is a vector quantity.

# Weightlessness

The weightlessness of a body is the state in which the body experiences that the body is not being attracted by any force

# Freefall

If a body is falling freely under the action of gravity alone neglecting air resistance, the motion is called freefall.

# Differences between g and G

g G

It is the acceleration produced on the body due to gravity It is the force of attraction between two unit masses separated by 1m distance

Its unit is m/s2 Its unit is Nm2/kg2

It is a vector quantity It is a scalar quantity

Its value changes from place to place. It is universal and is fixed

# Differences between Gravitation and Gravity

Gravitation Gravity

It is universal force It is not universal

It occurs between any two bodies in the universe For this one body must always be a planet or a satellite

# Differences between Mass and Weight

Mass Weight

It is the amount of substance contained in a body It is the force by which a body is attracted towards the center of the earth

It is a constant quantity It varies from place to place

It is a scalar quantity It is a vector quantity

Its unit is Kg Its unit is N

It is measured by beam balance It is measured by spring balance

# Exercise for Practice

Answer the following questions. Figure shows the marks for each question in SLC examination.

State Newton's law of gravitation. Calculate the force with which the Moon pulls every kilogram of water in our rivers given that the Moon is 3x 105 km away from Nepal and the mass of the Moon is 7x 10 22 kg. (Ans: 5.18x 10 -5 N) [1K+3.5HA = 4.5]

Define acceleration due to gravity 'g'. Explain why the value of 'g' is less at the top of Mt. Everest than at its bottom. [1K+2U =3]

Mention what is the relation of force of gravitation with masses of the objects and distance. If the mass of a planet is 1.9x10 26 kg and radius is 71x 10 6 m. What will be the gravitational field intensity of the planet? What will be the weight of a man of mass 60 kg on that planet? (G=6.67x10 -11 Nm2/kg2) [Ans: 25.13 N/kg, 1507.8N] [1+3=4]

Write down definition and the unit of acceleration due to gravity 'g'. Explain why the values of 'g' vary from place to place on the earth. [1.5+2=3.5]

State Newton's universal law of gravitation. What is the weight of a body during free fall?

Prove g [1+0.5+2=3.5]

Weight of an object is greater at the polar region than the equatorial region of earth, why? Calculate the gravitation force in between two objects of mass 25 kg and 20 kg if distance between them is 5m.[2+2=4 ] [Ans: 1.334x 10 -9N]

What is gravity? If mass of the sun is 2x 1033 kg, that of the earth is 6x 1024 kg and the distance between them is 1.5x 1011 m. What is the gravitational force produced between them?

(G = 6.67x 10-11 Nm2/kg2) [Ans: 3.557x 10 22N] [1+3=4]

If a body is dropped from the same height once in the equator an d then in the polar region, in which place will it fall faster? Explain with reason. What is weightlessness? Give a condition in which an object becomes weightless. [2+1+0.5=3.5]

List two differences between universal gravitational constant (G) and acceleration due to gravity (g). The earth's orbit is oval in shape. Explain how the magnitude of the gravitational force between the earth and the sun changes as the Earth moves from position 'A' to 'B' as shown in the figure below. [2+1.5=3.5]

In the formula g= GM/R2 what do G, M and R represent for? Calculate the mass of the Earth assuming that it is a sphere with radius 6.67x 10 6m. 1.5+2.5=4 [Ans: 6.536x 10 24 Kg]

Weight of a body is found less at the top of the mountain that at the bottom of it, why? The mass and the radius of Jupiter is 1.9x10 27 kg and 71x 106 m respectively, find out the acceleration due to gravity in it. [2+2.5=4.5] [Ans: 25.13 m/s2]

Write down the conclusion obtained from coin and feather experiment. Write down any two differences between mass and weight. 1+2=3

State Newton's law of gravitation. In which parts of the earth is the true weight of a body maximum and zero? Write two effects of gravity. 1+1+1=3

Define gravitational field intensity. If the mass of the moon is 7.2x1022 Kg and its radius is 1.7x10 6 m, calculate the gravitational field intensity of the moon. What will the weight of a person with mass 60 kg on the moon be?

Define Newton's law of gravitation. Why is it called universal law? A man of 75 kg is standing on the surface of the earth having the mass of 6x10 24 kg. If the radius of the earth is 6380 km, calculate the force of attraction between man and earth. (G=6.67x 10 -11 Nm2/kg2) 1+1+2.5 [Ans: 7.37x102N]

What is acceleration due to gravity? Establish the relation between due to gravity (g) and radius of the earth (R)1+2=3 [G=6.67x10 -11 Nm2 / kg 2] [1+2.5+1=4.5] [Ans:1.6N/Kg, 99.6N]

State Newton's law of gravitation. Calculate the change in gravitational force between two bodies when the distance between them is made double; keeping their mass constant. [2+2.5=4.5]

Define free fall? Why the apparent weight of freely falling object is zero? Find the weight of 10 kg object on the surface of the moon. [1+1+1=3] [Ans:16.6N]

What is gravity? If an object at a distance 6,400 km from the centre of earth weighs 10N, what will be its weight if it is lifted to 12,800 km from the centre of earth? Give a condition at which an object becomes weightless.

Write down two differences between weight and mass. If two objects of masses m1 and m2 are kept at a distance'd'. Prove that the gravitational force between them (F) =

It is defined as a push or pull that change or tends to change the state of rest or of uniform motion of a body along a straight line.

# Newton’s Universal law of gravitation

Consider a body of mass m1 attracts another body of mass m2 with a force F towards its centre O1. The body of mass m2 in turn attracts the body of mass m1 with the same force F towards its centre O2. Suppose the distance between their centers is‘d’ then, according to Newton’s universal law of gravitation, we have

F ∞ m1 x m2 … (i)

And F ∞ … (ii)

Combining these two equations (I) and (ii), we have

F ∞

Or, F = G …………. (iii)

Where G is called a proportionally constant or universal gravitational constant. The value of The G is determined form experiment.

Hence, the equation (iii) gives the measure of the gravitational force between two masses.

# Universal gravitational constant ‘G’

Universal gravitational constant ‘G’ can be defined as the force of gravitation that is exerted between two unit masses, separated from one another by a unit distance.

The SI unit of G is Nm2kg-2.

The approximate value of G is 6.67 10-11Nm2kg-2.

# Properties of G

The value of G is independent of the nature and chemical composition of the masses of the bodies, and the medium in which the bodies are occurred.

The value of G is unaffected by temperature and pressure.

# Consequences of gravitational force

The presence of solar system and planets revolve round the sun due to the presence of gravitational force.

The presence of atmosphere on the earth is due to the gravitational force.

The gravitational force of the earth keeps us firmly on the surface of the earth.

Tides in seas and oceans are due to the gravitational force of the sun and moon.

# Special features of gravitational force

The gravitational forces between two bodies constitute on action and reaction pair.

The gravitational force between two bodies does not depend upon the nature of the intervening medium.

The gravitational force between light bodies is extremely small and hence such smaller force is not felt in practice. However, it becomes appreciable in case of massive bodies.

# Gravity or weight

The force of attraction of the earth on a body is called force of gravity or simply the weight of the body on earth.

Let a body of mass m be placed on the surface of the earth of mass M as shown in the figure. The distance between them can be taken to be equal to the radius (R) of the earth. The weight (W) of the body on the surface of the earth is given by,

W = G …………….. (i) (

If m is kept constant,

W∞ ……….. (ii)

Equation (ii) shows that weight (W) of a body on the surface of a planet/ satellite is directly proportional to mass (M) of the planet /satellite. Greater the mass of the planet /satellite, larger its gravity is i.e., greater will be the weight of the body on the planet/satellite.

Equation (ii) also shows that weight (W) of a body on the surface of a planet/satellite is inversely proportional to the square of the radius (R) of the planet/satellite. The weight of the body will be less if it becomes large.

# Effects of gravity

We are able to stand up, run and perform other activities freely due to gravity of the earth.

Construction of building and bridges is possible due to the gravity of the earth.

There will be no atmosphere around the earth in the absence of gravity of the earth.

If a body is thrown upwards, its notion is opposed by gravity of the earth. So, it falls back to the earth.

Tides occur by the gravity of the moon on ocean water.

# Acceleration due to gravity

Acceleration due to gravity is defined as the acceleration produced in a freely falling body due to the force of gravity of the earth towards its center. It is denoted by g and its average value is 9.8 m/s2.

# Relation between Radius and Gravity

Let M be the mass of the earth and R its radius, then the force of attraction on a body of mass m on its surface as given by the Newton’s Universal law of gravitation is

But, the force with which the body is attracted towards the center of the earth is the weight of the body.

As (i) and (ii) represents the same force, we get,

This is the expression for the acceleration due to gravity. The value of g on the surface of the earth is

Independent of mass of the body

Depends on the mass of the earth and the radius

iii. Suggests that the value of g at a particular place is constant.

# Variation in the value of g

Variation due to shape [ On the surface]

Variation with height

Variation with depth

…………………(c)

# Gravitational field and Gravitational field intensity

The space around a mass over which it can exert gravitational force on other masses is called the gravitational field of the mass.

The gravitational field intensity at a point in the gravitational field is defined as the force experienced by unit mass placed at that point. Its unit is N/Kg.

Gravitational field intensity I and acceleration due to gravity g are one and the same thing, so

# Mass

The amount of substance contained in a body is called the mass. The mass of the body is measured by using a physical balance or beam balance. It unit if kg in SI. The mass of the body is dependent upon the number of atoms and average mass of atoms present in the body.

# Weight

The weight of a body is defined as the force with which it is attracted towards the center of the earth. SI unit of weight is Newton (N). Its value changes from place to place as it depends on the acceleration due to gravity (g). It is a vector quantity.

# Weightlessness

The weightlessness of a body is the state in which the body experiences that the body is not being attracted by any force

# Freefall

If a body is falling freely under the action of gravity alone neglecting air resistance, the motion is called freefall.

# Differences between g and G

g G

It is the acceleration produced on the body due to gravity It is the force of attraction between two unit masses separated by 1m distance

Its unit is m/s2 Its unit is Nm2/kg2

It is a vector quantity It is a scalar quantity

Its value changes from place to place. It is universal and is fixed

# Differences between Gravitation and Gravity

Gravitation Gravity

It is universal force It is not universal

It occurs between any two bodies in the universe For this one body must always be a planet or a satellite

# Differences between Mass and Weight

Mass Weight

It is the amount of substance contained in a body It is the force by which a body is attracted towards the center of the earth

It is a constant quantity It varies from place to place

It is a scalar quantity It is a vector quantity

Its unit is Kg Its unit is N

It is measured by beam balance It is measured by spring balance

# Exercise for Practice

Answer the following questions. Figure shows the marks for each question in SLC examination.

State Newton's law of gravitation. Calculate the force with which the Moon pulls every kilogram of water in our rivers given that the Moon is 3x 105 km away from Nepal and the mass of the Moon is 7x 10 22 kg. (Ans: 5.18x 10 -5 N) [1K+3.5HA = 4.5]

Define acceleration due to gravity 'g'. Explain why the value of 'g' is less at the top of Mt. Everest than at its bottom. [1K+2U =3]

Mention what is the relation of force of gravitation with masses of the objects and distance. If the mass of a planet is 1.9x10 26 kg and radius is 71x 10 6 m. What will be the gravitational field intensity of the planet? What will be the weight of a man of mass 60 kg on that planet? (G=6.67x10 -11 Nm2/kg2) [Ans: 25.13 N/kg, 1507.8N] [1+3=4]

Write down definition and the unit of acceleration due to gravity 'g'. Explain why the values of 'g' vary from place to place on the earth. [1.5+2=3.5]

State Newton's universal law of gravitation. What is the weight of a body during free fall?

Prove g [1+0.5+2=3.5]

Weight of an object is greater at the polar region than the equatorial region of earth, why? Calculate the gravitation force in between two objects of mass 25 kg and 20 kg if distance between them is 5m.[2+2=4 ] [Ans: 1.334x 10 -9N]

What is gravity? If mass of the sun is 2x 1033 kg, that of the earth is 6x 1024 kg and the distance between them is 1.5x 1011 m. What is the gravitational force produced between them?

(G = 6.67x 10-11 Nm2/kg2) [Ans: 3.557x 10 22N] [1+3=4]

If a body is dropped from the same height once in the equator an d then in the polar region, in which place will it fall faster? Explain with reason. What is weightlessness? Give a condition in which an object becomes weightless. [2+1+0.5=3.5]

List two differences between universal gravitational constant (G) and acceleration due to gravity (g). The earth's orbit is oval in shape. Explain how the magnitude of the gravitational force between the earth and the sun changes as the Earth moves from position 'A' to 'B' as shown in the figure below. [2+1.5=3.5]

In the formula g= GM/R2 what do G, M and R represent for? Calculate the mass of the Earth assuming that it is a sphere with radius 6.67x 10 6m. 1.5+2.5=4 [Ans: 6.536x 10 24 Kg]

Weight of a body is found less at the top of the mountain that at the bottom of it, why? The mass and the radius of Jupiter is 1.9x10 27 kg and 71x 106 m respectively, find out the acceleration due to gravity in it. [2+2.5=4.5] [Ans: 25.13 m/s2]

Write down the conclusion obtained from coin and feather experiment. Write down any two differences between mass and weight. 1+2=3

State Newton's law of gravitation. In which parts of the earth is the true weight of a body maximum and zero? Write two effects of gravity. 1+1+1=3

Define gravitational field intensity. If the mass of the moon is 7.2x1022 Kg and its radius is 1.7x10 6 m, calculate the gravitational field intensity of the moon. What will the weight of a person with mass 60 kg on the moon be?

Define Newton's law of gravitation. Why is it called universal law? A man of 75 kg is standing on the surface of the earth having the mass of 6x10 24 kg. If the radius of the earth is 6380 km, calculate the force of attraction between man and earth. (G=6.67x 10 -11 Nm2/kg2) 1+1+2.5 [Ans: 7.37x102N]

What is acceleration due to gravity? Establish the relation between due to gravity (g) and radius of the earth (R)1+2=3 [G=6.67x10 -11 Nm2 / kg 2] [1+2.5+1=4.5] [Ans:1.6N/Kg, 99.6N]

State Newton's law of gravitation. Calculate the change in gravitational force between two bodies when the distance between them is made double; keeping their mass constant. [2+2.5=4.5]

Define free fall? Why the apparent weight of freely falling object is zero? Find the weight of 10 kg object on the surface of the moon. [1+1+1=3] [Ans:16.6N]

What is gravity? If an object at a distance 6,400 km from the centre of earth weighs 10N, what will be its weight if it is lifted to 12,800 km from the centre of earth? Give a condition at which an object becomes weightless.

Write down two differences between weight and mass. If two objects of masses m1 and m2 are kept at a distance'd'. Prove that the gravitational force between them (F) =

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