**Notes of chapter: Gravitation are presented below. Indepth notes along with worksheets and NCERT Solutions for Class 9.**

**(1)Centripetal force –**

**Centripetal force** is force which acts at the center of the circular path and causes change in the acceleration and velocity of the object.

**Eg:- (a)**A stone tied at an end of a string and move on a circular path with constant magnitude but continuously changing velocity and acceleration. The centripetal force on the stone is directed towards the center (Our hands) which is providing force on the stone.

**(b)** A bike rider movement on a circular path.

**(c)** The movement of the Moon around the Earth.

The Moon moves in orbit around the Earth. The motion of the Moon is due to centripetal force which is provided by the force of attraction or gravitational force of center of the Earth.

In the absence of centripetal force, the object will move in a straight line which is tangent to the circular path.

**(2) Gravitational force-**

The **gravitational force** is a natural force which attracts every object towards the Earth.

**Eg:- (a)** The falling of apple.

The falling apple attracted towards the Earth.

And the apple also attracted the Earth (according to third law of motion).

But F = ma (Second law of motion)

F ∝ m

Therefore, force is directly proportional to the mass of the object.

And mass of the apple is negligible than mass of the Earth.

We can not see the Earth is moving or falling towards the apple.

But, we can see an apple is moving or falling towards the Earth.

**(b)** All planets move around the Sun due to gravitational force otherwise they will go straight. Planets and the Sun attract each other with their gravitational force. When gravitational force of the Sun is greater than the gravitational force of the planet, the planet will attract towards the Sun.

**(3) Universal Law of gravitation-**

Every object in the universe attracts each other with a force.

The force along the line joining the centers of two objects is proportional to the product of their masses and inversely proportional to square of distance between them is called **universal law of gravitation.**

**(3) Universal law of gravitation-**

The **universal law of gravitation** explained many phenomena which are

**(i)** the force that bind us to the Earth.

**(ii)** the motion of the Moon around the Earth.

**(iii)** the motion of the planets around the Sun.

**(iv)** the tides due to the Moon and the Sun.

**(4) free fall-**

**Free fall** of any object is the motion of the object which fall towards the Earth due to gravitational force.

**Eg:-** **(i)**Stone throw in upward direction after reaching at a height it moved downward due to gravitational force.

**(ii)**Fall from parachute before opening it.

When object starts falling its direction does not change. The object is always towards the Earth.

But initial velocity is zero.

Acceleration which is caused due to gravitational force of the Earth is constant.

It us denoted by ‘g’ and its value is 9.8 m/s^{2}.

The Earth is not a complete sphere.

The radius of the Earth increased from poles to equator, therefore, value of g decreased from poles to equator.

**(i)** The value of g is highest at the poles.

**(ii)** The value of g is lowest at the equator.

All equations for the uniformly accelerated motion of the objects can be used with constant acceleration due to gravitational force.

**Eg:-** An object dropped from a point which is at 10 meter distance from the Earth. The object reaches to the earth in 1 second. Take g = 10 m/s^{2}

Find

**(i)** Initial velocity of the object.

**(ii)** Velocity of the object before touching the ground.

**Ans-**

s = 10 m

Time, t = 1 s

g = a = 10 m/s^{2}

**(i)** Initial velocity of the object, u = 0 m/s

**(ii)** v = u + at

v = 0 + 10 (1)

v = 10 m/s

Hence, velocity of the object before touching ground is 10 m/s towards the Earth.

**(6) Mass-**

**Mass** is the measure of amount of the object which resist a change in its state of motion or rest. In simple words mass is measure of inertia.

Mass of an object is constant and does not change from place to place.

**(7) Weight-**

**Weight **of an object is the force with which it attracts towards the Earth.

Let the mass of the object = m

The gravitational force due to gravity = g m/s^{2}

Weight of the object, W = Mass of the object Acceleration due to gravity

W = mg…(1)

But we know, F = ma

Where, F is force and a is acceleration of the object

If acceleration is constant then a = g

F = mg…(2)

W = F (From equation 1 and 2)

The unit of the weight is newton.

The weight is a force which

**(i)** acts vertically downward and

**(ii)** has magnitude and direction.

We know,

W = mg

Where g is constant

W ∝ m

Therefore, at a given place, weight of an object can be used as a measure of its mass.

The differences between mass and weight are tabulated below –

SN |
Mass |
Weight |

1 |
Constant everywhere | Can be change |

2 |
Can not change if value of g changes on different planets or anywhere | Can change according to acceleration on different places planets or any where. |

3 |
Mass is not equal to force of attraction of the earth on an object | Weight is equal to force of attraction of the earth on an object |

4 |
Its unit is kg. | Its unit is newton. |

** (8)** The weight of an object varies on different planet due to different gravitational force.

**Eg:-** We multiply mass with acceleration of the object due to earth’s gravitational force to get weight of the object on the Earth. But, on moon or on other planets we multiply mass of the object with acceleration of the object due to gravitational force of the moon or the planet where the object is located to know weight of the object.

Necessary data to calculate ratio of weight of the object on moon and on earth

SN |
Celestial Body |
Mass (kg) |
Radius (m) |

1 |
Earth | 5.98 10^{24} |
6.37 10^{6} |

2 |
Moon | 7.36 10^{22} |
1.74 10^{6} |

**(9) Thrust-**

**Thrust **is a force acting on an object perpendicular to the surface.

**Eg:-** If we stand on the sand, we will go inside the sand. It happens because of our small area of feet which is in contact of sand. The force which is equal to our weight applied on area of the feet. The contact area (Our body) with sand is very small. Therefore, we applied high pressure on the sand and go deep inside the sand.

To fix a poster on a bulletin board, we press board pins on the board. In this way, we apply force perpendicular to the surface area of the board.

**Eg:-** If we lay down on the sand, we will not go inside the sand. It happens because of our large area which is in contact of sand. The force which is equal to our weight applied on area of our body. The contact area (Our body) with sand is very large .Therefore, we applied low pressure on the sand and do not go deep inside the sand.

**(11)** Fluids (Gases and liquids) also have weight and they also exert pressure on the base and walls of the container in which they are enclosed.

**(12) Buoyancy-**

**Buoyancy** is an upward force exerted by the fluid in which a body immersed. It is also called as **upthrust or buoyant force**.

The magnitude of this buoyant force depends on the density of the fluid.

The SI unit of buoyancy is newton.

**(13)** **Objects sink in water or fluid.**

**Eg:-** An iron nail sinks in water.

**Explanation – (a)** The nail experiences two forces acting on it simultaneously. First, the gravitational force acting downwards on the nail exerted by the Earth. Second, the buoyant force acting upward on the nail exerted by the water. If downward force is greater than the upward force, the nail sinks.

**(b)** The density of the nail is very high in comparison of the density of the water. Therefore, the upthrust force or buoyant force of water on nail is less than the weight of the nail. Hence, it sinks.

**(14)** **Objects float in the water or liquid.**

**Eg:-** A cork floats on the water.

**Explanation- (a)** The cork experiences two forces acting on it simultaneously. First, the gravitational force acting downwards on the cork exerted by the earth. Second, the buoyant force acting upward on the cork exerted by the water. If downward force is less than the upward force, the cork floats.

**(b)** The density of the cork is lesser than the density of the water. Therefore, the upthrust force or buoyant force of water on cork is higher than the weight of the cork. Hence, it floats.

**(15) The Archimedes’ principle **is stated as follows-

**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.**

**Eg:-** Tie a stone at the end of the rubber string. Suspend the stone by holding the other end. Note the elongation of the string. Dip the string in the water. Now note the elongation of the string. It will decrease as the stone is gradually lowered in water. It means that the upward force (Buoyant force) is acting on the stone. As a result, the net force on the stone decreases and hence, the elongation also decreases.

**Applications of the Archimedes’ principles**–

**(i)** It is used in designing ships and submarines.

**(ii)** Lactometers which are used to determine the purity of a sample of milk and hydrometers used for determining density of liquids.

**Helping Topics**