Gravitation Short Notes Class 9 Science Chapter 10

Brief Notes on Gravitation | Class 9

Overview

The force of attraction between any two bodies in the universe is known as gravity. This force controls the motion of celestial bodies and keeps us rooted to the earth.

The Universal Law of Gravitation

The universal law of gravitation states that every particle in the universe is drawn to every other particle with a force that is inversely proportional to the square of the distance between their centres and directly proportional to the product of their masses.

The Universal Law of Gravitation states:

-->Every mass in the cosmos is drawn to every other mass by a force that is inversely proportional to the square of their distance from one another and directly proportional to the product of two masses.

• Let's assume masses (M) and (m).

F = (GMm)/d2 F ∝ M×m F ∝ 1/d2 F ∝ Mm/d2

where G, also referred to as the gravitational constant,

Value of G = 6.67×10^-11 Nm²/kg²

→ If F is in Newtons, m is in kilograms, and d is in meters, then G can be computed as follows: 

G = (F×d2)/Mm, meaning that the unit will be Nm2/kg2.

The Universal Law of Gravitation's Significance

(i) The gravitational pull that ties us to the earth; 

(ii) The moon's orbit around the earth; and 

(iii) The planets' orbits around the Sun.

(iv) The tides brought on by the Sun and Moon.

Falling Free

• When an object falls to the earth only due to gravity and without the assistance of any additional forces, such as air, this is known as free fall.
• When something is dropped and only gravity pulls it down, it moves.
• The direction does not vary throughout this free fall, but the velocity does, which is known as acceleration due to gravity. The letter "g" stands for it.
•  It is measured in the same unit as acceleration (m/s2).

Acceleration due to gravity

• The acceleration that an object experiences as a result of a huge body like Earth's gravitational pull is known as gravitational acceleration. 
• The symbol (g) represents this acceleration.

The value of (g) at the Earth's surface:

• At the Earth's surface, the gravitational acceleration (gg) is roughly:

g = 9.81 m/s² g = 9.81 m/s²

Newton's Universal Law of Gravitation provides the value of (g):

                                g=GM/R2.​

where:

• (G) is equal to 6.674×10−11m3kg−1s−2, and
•  (M) equals is the Earth's mass (M=5.972×1024 kg).
• (R) is the Earth's radius (R=6.371×106m).

The connection and distinction between "G" and "g"
G is the gravitational constant.
g = Gravitational Acceleration
g is equal to GM/R2.

Difference between G (Gravitational constant) and g (Acceleration due to gravity)

	$G$ (Gravitational Constant)	$g$ (Acceleration due to Gravity)
	$G$ is a universal constant that quantifies the strength  of gravity between two masses.	$g$ is the acceleration  experienced by an object due to the  gravitational force acting on it, typically  near the Earth's surface.
	$G\approx 6.674\times 10^{-11}{\text{N m}}^2\mathrm{/}{\text{kg}}^2$	$g\approx 9.81{\text{m/s}}^2$ at the Earth's surface.
	Used in the formula for  gravitational force between two masses: $F=G\frac{m_1{m}_2}{r^2}$	Used to calculate the  force of gravity acting on an object, $F=m\cdot g$  (where $m$ is mass).
	N m²/kg² (newton meter  squared per kilogram squared)	m/s² (meters per second squared)
	A constant value that applies universally, regardless  of location or masses involved.	A variable that can change  depending on altitude and local gravitational field (e.g., it differs from Earth to another planet).

Mass

• The amount of matter that makes up a thing is its mass.
• It has magnitude but no direction, making it a scalar quantity.
• The kilogramme (kg) is the SI unit of mass.
• Milligrammes (mg) and grammes (g) are additional units.
• Inertia: An object's resistance to changes in its state of motion is measured by its mass.
• Constant: No matter where an object is in the cosmos, its mass stays constan

Weight

• The force that pulls an object towards the Earth's (or any other celestial body's) centre is known as its weight.
• Since it has both magnitude and direction (in the direction of the Earth's centre), it is a vector quantity.

 formula: W=mg

where the,

• weight is denoted by (W).
• (m) represents the object's mass.
• (g) is the gravitational acceleration.

• The SI unit of weight is the Newton (N), since weight is a force.

An object's weight on the moon

The weight of an object on the Moon can be calculated using the formula:

$$$$Weight on Moon=Weight on Earth×16

​

This is because the gravitational force on the Moon is approximately $\frac{1}{6}$ that of Earth's gravity.

For example, if an object weighs 60 kilograms on Earth, its weight on the Moon would be:

$$$$Weight on Moon=60 kg×16≈10 kg

Pressure and Thrust

• Definition of Thrust: Thrust is the force that propels an item forward. It functions perpendicular to the object's surface.
• Formula: The thrust (FtF t) can be written as follows:

Ft=m×a

F t = m×a, where aa is the acceleration and mm is the object's mass.

• Examples: Thrust is important in various applications like:
  • The thrust produced by rockets to propel them into space.
  • The push of a person when pushing a shopping cart.

Pressure:-

• Definition: The force exerted per unit is known as pressure. It characterises the degree of force concentration over a specific area.
• Formula: The following formula can be used to determine pressure (PP): 

       P=AF​

where ,

$F$ is the force applied and $A$

$A$ is the area over which the force is distributed.​

• Units: One Newton per square metre (N/m2) is equivalent to one Pascal (Pa), the SI unit of pressure.

• Examples: Pressure can be observed in:

  • The pressure exerted by the heels of a person standing.
  • Air pressure, which is the weight of the air above us in the atmosphere.
  • Water pressure, which increases with depth in a fluid.

Buoyancy

The upward force that a fluid applies to an object submerged in it is known as buoyancy. It permits things to sink or float.

Density

↑ An object's density is its mass per unit volume.

→ Density (d) = Mass(M)/Volume(V) if M is the mass and V is the volume.
• The SI unit is kg/m3.

Archimedes Principle 
According to Archimedes' Principle:

"A body experiences an upward force (buoyant force) equal to the weight of the fluid displaced by the body when it is fully or partially submerged in it."

Archimedes' Principle Applications

(i) It is employed to ascertain the relative densities of various substances.
(ii) Ships and submarines are designed using it.
(iii) This idea underlies the construction of lactometers and hydrometers.

This is the reason why a ship composed of steel and iron floats in water but a little iron fragment sinks.

The relative density

In relation to Density can be defined as the ratio of a substance's density to that of water. Since it lacks units, it is a dimensionless quantity.

The formula

RD = Density of substance/Density of water