## Force Class 10 | SEE Physics Notes

### Force:

**Definition: **The force is an external factor or agency which change or tend to change the state of objects.

- The definition of force is given by the first law of motion given by Newton.
- Its measurement is given by the second law of motion.
- F = m.a = Mass * Acceleration due to gravity.
- Its SI unit is Newton.

### Gravitation:

**Definition:**** **The force of attraction between two bodies is called Gravitation.

**Diagram:**- Gravitation is the force and its unit is Newton (N).
- It is denoted by F.
- F = GM
_{1}M_{2}/d^{2}

Where,

M=m = Mass

d= Distance

G= Universal Gravitational Constant.

= 6.61 × 10^{-11}N m^{2}kg^{-2}**Examples:**

a) Table and Book

b) Pen and Copy

c) Tree and Building

d) Vehicle and road

e) Nucleus and electrons, etc.

### Gravity

**Definition:**The gravity is the force of attraction between two bodies in which at least one should be a heavenly body.**Diagram:**- F= GM
_{1}M_{2}/d^{2}

Where,

M= Mass of Heavenly body

m= Mass of object

d= Distance

**Examples:**

a) Moon and Ocean

b) Earth and airplane

c) Earth and Sun

d) Earth and Moon, etc.

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### Universal Law of Gravitation:

- It is given by Sir Issac Newton.
- The force of attraction is directly proportional to the square of the distance between two bodies i.e F
- The force of attraction is inversely proportional to the square of the distance between two bodies i.e F ∝ 1/d
^{2}

From a & b

F ∝ GM_{1}M_{2}/d^{2 }or, F =GM_{1}M_{2}/d^{2} - Where,

M_{1}and M_{2}= Mass

d= Distance

G= Universal Gravitational Constant

= 6.61 × 10^{-11}N m^{2}kg^{-2}

**Universal Gravitational Constant (G): **

we know that,

F = GM_{1}M_{2}/d^{2}

or, F = G×1×1/1^{2}

- The universal gravitation constant (G) is the force of attraction when two bodies of mass 1Kg is a parted by 1m.

G = F×d^{2}/M_{1}M_{2}

or, G = Nm²/kg²

or, G = Nm²/kg^{-2}

**1Q. Find the force of gravitation when the distance is doubled?**

Case – 1

F_{1}= GM_{1}M_{2}/d^{2}

Case – 2

F_{2}= GM_{1}M_{2}/(2d^{2}) = GM_{1}M_{2}/d^{2} × 1/4

= F_{1} × 1/4

= F_{1}/4

**2Q. Find the force of Gravitation when the distance is halved?**

Case – 1

F_{1}= GM_{1}M_{2}/d^{2}

Case – 2

F_{2}= GM_{1}M_{2}/(2d^{2}) = GM_{1}M_{2}/d^{2} × 4

= F_{1} × 4

= 4F_{1}

**3Q. What is the value if gravitation when mass is doubled?**

Case – 1

F_{1}= GM_{1}M_{2}/d^{2}

Case – 2

M_{2} = 2M_{2}

F_{2}= GM_{1}M_{2}/(2d^{2}) = GM_{1}×2M_{2}/d^{2
}= GM_{1}2M_{2}×2/d^{2
}= F_{1}×2

### Acceleration due to gravity (g):

**Definition: **The acceleration produced due to the gravity of a planet or heavenly body is called Acceleration due to gravity.

- It is denoted by ‘g’.
- Its value of sea level: 9.81 m/s² (SI unit)

: 9.81 cm/s² (CGS unit) - g = GM/R²

where,

G= Universal gravitational constant

= 6.61 × 10^{-11}N m^{2}kg^{-2}

M= Mass of planet (kg)

R= Radius (m)

= Distance from center of planet to center of object. - Case I

- g= GM/R² =GM/(R+H) = GM/(R+O) =GM/R²
- Case II

- Prove:

g∝1/R²

or g= GH/R² **Statement:**The object of mass = ‘m’ is placed at height of ‘n’ from the surface of the earth which Mass and Radius are ‘M” and ‘R’ respectively.**Diagram:**

- The weight of an object is counterbalanced by force of gravity.

~~mg~~= GM~~m~~/R²

or, g= GM/R²

or, g∝ 1/R²

Where,

G= Constant

M= Constant

*Proved.* **Prove**

g= GM/(R+H)²

or, g∝ 1/(R+H)²**Statement:**The object of mass = ‘m’ is placed at height of ‘n’ from the surface of the earth which Mass and Radius are ‘M” and ‘R’ respectively.**Diagram:**

- The weight of an object is counterbalanced by force of gravity.

~~mg~~= GM~~m~~/(R+H)²

or, g= GM/(R+H)²

or, g∝1/(R+H)²

*Proved.*Where,

G= Constant

M= Constant

### Factor on which ‘g’ depends:

- g∝M: The g depends on the mass of the planet.
- g∝1/R²: THe ‘g’ depends on the distance between the center of planet and center of an object.
- It doesn’t depend on Mass of an object.

### Differentiate between on ‘G’ and ‘g’.

The differentiate between on ‘G’ and ‘g’ are given below:

It is the force of gravitation between any two objects each of unit mass separated by unit distance.

‘G’ | ‘g’ |
---|---|

It is the acceleration produced on a freely falling object toward the earth or planet. | |

Its SI unit is m/s^{2}. | Its SI unit is Nm^{2}kg^{2}. |

It is a vector quantity. | It is a scalar quantity. |

### Differentiate between on Gravitational force and force of gravity.

The differentiate between on Gravitational force and force of gravity are given below:

Gravitational force | Force of Gravity |
---|---|

Gravitational is the force of attraction between any two objects of the universe due to their masses. | Gravity is the force with which the earth or any heavenly body attracts other objects towards its center. |

It depends upon the product of their masses and the distance between them. | It depends upon its mass and its radius. |

### Freefall:

**Definition: **The freefall is the natural phenomena in which an object falls on the surface of a planet with acceleration due to gravity (g).

**Diagram:**

- In the state of freefall, apparent weight is zero(0).
- The heavenly bodies show freefall because these have negligible air resistance.

Examples: Fruit, Stone, Hail, Rock, etc. - The light bodies don’t show freefall due to air resistance.

Examples: Cotton, Feather, Paper, leaf, etc. - In the surface of the moon, heavy as well as light object show freefall due to lack of air resistance.
**Parachute:**In beginning, it is a bundle of plastic and shows freefall.

After sometimes, it is opened and its volume is increased. It doesn’t show freefall due to air resistance.

### Weightlessness:

**Definition: **The weightlessness is a condition in which the apparent weight of object becomes zero due to freefall.

R(Resultant force/ Apparent weight)

Weight (w=mg)

R= mg – mg¹

=m (g-g¹) [In freefall g= g¹]

=m(g-g)

=m × 0

=0

**Answer these questions:**

- Define the terms gravity and gravitation.

Ans: The**gravity**is the force of attraction between two bodies in which at least one should be a heavenly body. whereas**Gravitational**is the force of attraction between any two objects of the universe due to their masses. - State Newton’s Universal law of gravitation.

Ans: Newton’s Universal law of gravitation states that the force of gravitation between any two bodies is directly proportional to the product of their masses and inversely proportional to the square of a distance between their centers. - Write down the relation of gravitational force with masses of bodies and their distance?

Ans: The relation of gravitational force with masses of bodies and their distance is F = GM_{1}M_{2}/d^{2}. - What is gravitational constant? Write down its value.

Ans: Gravitational constant is the force of gravitation between two bodies each of unit mass separated by unit distance.

Its value is 6.61 × 10^{-11}N m^{2}kg^{-2}. - Acceleration due to gravity on the moon is 1.67 m/s², what does it mean?

Ans: Acceleration due to gravity on the moon is 1.67 m/s² it means that mass of the moon is 7.2×10²²kg and its radius is 1.7×10^{6}m. - Name two factors that affect the gravitational force.

Ans: Two factors that affect gravitational force are:

a) Mass and Distance.

b) The distance between the two objects, etc. - What is the value of acceleration due to gravity at the equatorial region of the earth?

Ans: The value of acceleration due to gravity at the equatorial region of the earth is 9.78m/s². - How does ‘g’ vary from place to place?

Ans: ‘g’ varies from place to place because its value of ‘g’ at the pole of the earth is more but is less at the equator. - What is the factor that affects gravity?

Ans: Factors that affect gravity are:

a) Water flows in the river.

b) It causes acceleration to a falling object, etc. - Is there any place in the earth where the value of ‘g’ is zero?

Ans: The center of the earth where the value of ‘g’ is zero. - What will be the change in gravitational force if the distance between the bodies is halved?

Ans: Mass remains the same but the distance change when gravitational force if the distance between the bodies is halved. - Under what condition, a coin and a feather fall together? What is the acceleration of the feather and the coin at that instant?

Ans: If there is no any air to resist the falling of a body, coin and a feather fall together.

The acceleration of the feather is 0m/s at the instant. - Define the gravitational field? and gravitation field intensity.

Ans: The space around a planet or any heavenly body up to which its gravity can be felt is called gravitation.

The force of the gravity experienced by a unit mass placed at that point is called Gravitation field intensity. - Define Weightlessness.

Ans: The weightlessness is a condition in which the apparent weight of object becomes zero due to freefall. - What is freefall? What will be the weight of a body at this condition?

Ans: The freefall is the natural phenomena in which an object falls on the surface of a planet with acceleration due to gravity (g).

The weight of a body will be zero at this condition. - In which condition does an object become weightlessness?

Ans: A body feels weightlessness during freefall due to lack of reaction force condition an object becomes weightlessness

**Differentiate between: **

a)Gravity and acceleration due to gravity.

Ans: The differentiate between Gravity and acceleration due to gravity are given below:

The acceleration produced due to the gravity of a planet or heavenly body is called Acceleration due to gravity. It is the cause for the acceleration due to gravity. It is not affected.

Gravity | Acceleration due to gravity |
---|---|

Gravity is the force with which the earth or any heavenly body attracts other objects towards its center. | |

Its SI unit is m/s^{2}. | Its SI unit is Newton. |

It is the effect of gravity. |

b) Mass and weight

The differentiate between on Mass and weight are given below:

The amount of gravity by which an object is pulled by the earth or any planet towards its center.

Mass | Weight |
---|---|

The total matter contained in a body is called Mass. | |

Its SI unit is Kilogram. | Its SI unit is Newton. |

It is a scalar quantity. | It is a vector quantity. |

c) Weightlessness and freefall

Ans: The differentiate between on Weightlessness and freefall are given below:

Weightlessness | Freefall |
---|---|

The weightlessness is a condition in which the apparent weight of an object becomes zero due to freefall. | The freefall is the natural phenomena in which an object falls on the surface of a planet with acceleration due to gravity (g). |

A body feels weightlessness during freefall due to lack of reaction force. | In the state, if freefall apparent weight is zero. |

d) I and g

Ans: The differentiate between on I and g are given below:

It is the force of gravitation between any two objects each of unit mass separated by unit distance.

I | g |
---|---|

The force of gravity experienced by a unit mass placed at the point. | |

Its formula is I= GM/d^{2} | Its formula is g= GM/R^{2} |

**Prove that:**

a) F= Gm¹m²/d²

Solution:

F∝M_{1} M_{2}—i

F∝1/d²—ii

F∝M_{1} M_{2}/d^{2}

or, F= GM_{1} M_{2}/d

*Proved.*

b) g= GM/R²

**Solution:**

**Statement: **The object of mass =Sc ‘m’ is placed at height of ‘n’ from the surface of the planet which Mass and Radius are ‘M” and ‘R’ respectively.

**Diagram:**

The weight of the object is counterbalanced by force of gravity.

~~mg~~= GM~~m~~/R²

or, g= GM/R²

**Give reasons:**

- Newton’s law of gravitation is known as the universal law.

Ans: Newton’s law of gravitation is known as the universal law because Newton’s law of gravitation is true thought about the universe, it is true not only on the earth but on the moon, Jupiter or in space too. - A body falls faster at polar region than at the equatorial region of the earth.

Ans: A body falls faster at polar region than at the equatorial region of the earth because of the weight of object calculated by w=m×g. Mass of a body remains constant but a value of ‘g’ is inversely proportional to the square of the radius of the earth. - The force of gravitation between any two ordinary masses is not remarkable.

Ans: The force of gravitation between any two ordinary masses is not remarkable because the gravitational force increases with the increase in the mass of bodies. - The value of ‘g’ varies from place to place on the surface of the earth.

Ans: The value of ‘g’ varies from place to place on the surface of the earth because the value of ‘g’ pf the earth is inversely proportional to the square of its radius i.w g∝1/R². - The weight of an object is greater at the polar region than the equatorial region of the earth.

Ans: The weight of an object is greater at the polar region than the equatorial region of the earth because the weight of a body is calculated by using a formula, weight (f), mass (m), the acceleration due to gravity (g). Mass of the body remains constant but a value of ‘g’ differs from place to place. Value of ‘g’ is inversely proportional to the square of the radius of the earth. - The probability of getting hurt is more when a person jumps from a large height.

Ans: The probability of getting hurt is more when a person jumps from a large height because of more gravitational force in the falling body in large height. - The moon doesn’t have an atmosphere.

Ans: The moon doesn’t have an atmosphere because it has less gravity. - It is difficult to lift a large stone but easy to lift a smaller one and having more mass has more gravity.

Ans: It is difficult to lift a large stone but easy to lift a smaller one and having more mass has more gravity because the large stone has higher mass than smaller one and having more mass has more gravity. - It is difficult to drink water inside an artificial satellite in the space.

Ans: It is difficult to drink water inside an artificial satellite in the space because an artificial satellite has no gravity and inside the spaceship, it feels weightlessness. - A person can jump higher distance on the moon’s surface than on the earth.

Ans: A person can jump higher distance on the moon’s surface than on the earth because Gravity of the moon is six times less than that of the earth, so man is attracted by the moon with six-time lesser gravity than by earth. - If a coin and a feather are dropped from the same height at the same time on the moon’s surface, they fall together.

Ans: If a coin and a feather are dropped from the same height at the same time on the moon’s surface, they fall together because Gravity of the moon is six times less than that if the earth, therefore coin, and a feather fall together. - The mass of the Jupiter is 319 times more than that of the earth but its gravity is only 2.5 times more than that of the earth.

Ans: The mass of the Jupiter is 319 times more than that of the earth but its gravity is only 2.5 times more than that of the earth because the weight of a body on a planet is the product of the mass of the body and acceleration due to the gravity of the planet. - The parachutists are not hurt when they jump out of an airplane.

Ans: The parachutists are not hurt when they jump out of an airplane because in beginning it is a bundle of plastic, and shows freefall. After sometimes, it is opened and its volume is increased. It doesn’t show freefall due to air resistance. - When a person jumps from an airplane with a parachute he can safely on the earth surface but it is not possible on the moon.

Ans: When a person jumps from an airplane with a parachute he can safely on the earth surface but it is not possible on the moon because the moon has no atmosphere. so the parachute show freefall due to air resistance.

- Newton’s law of gravitation is known as the universal law.