**CBSE NOTES CLASS 9 SCIENCE CHAPTER 10**

**GRAVITATION**

**Centripetal Force**

The force directed towards the centre of the circle is called centripetal force.

**Tangent to a circle**

A straight line that meets the circle at one and only one point is called a tangent to the circle.

**Inverse Square Law**

Any physical law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity.

**Gravitation**

Gravitation is the force of attraction between two objects in the universe.

**Universal Law of Gravitation**

Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them.

The force is along the line joining the centres of two objects.

That is,

$$\mathrm{F}\propto \mathrm{M}\times \mathrm{m}\mathrm{}$$

And

$$\mathrm{F}\propto \frac{1}{{\mathrm{d}}^{2}}$$

Therefore, we can write,

$$\mathrm{F}=\mathrm{}\mathrm{G}\frac{\mathrm{}\mathrm{M}\times \mathrm{m}}{{\mathrm{d}}^{2}}$$

Where, G is the universal gravitational constant.

The SI unit of G is N m^{2 }kg^{-2}.

The value of G is 6.673×10^{-11} N m^{2 }kg^{-2}

The law is **universal** in the sense that it is applicable to all bodies, whether the bodies are big or small, whether they are celestial or terrestrial.

Universal law of gravitation is an **inverse square law.**

**Importance of Gravity**

- the force that binds us to the earth;
- the motion of the moon around the earth;
- the motion of planets around the Sun;
- The tides due to the moon and the Sun.

**Free Fall**

Whenever objects fall towards the earth under the gravitational force alone, it is said to be in free fall.

While falling, there is no change in the direction of motion of the object but there will be a change in the magnitude of the velocity.

When an object falls towards the ground from a height, its velocity changes during the fall. The acceleration is due to the earth’s gravitational force and is called the acceleration due to the gravitational force of the earth (or acceleration due to gravity). It is denoted by **g**.

$$\mathrm{F}=\mathrm{}\mathrm{G}\frac{\mathrm{}{\mathrm{M}}_{\mathrm{E}}\times \mathrm{m}}{{\mathrm{d}}^{2}}\mathrm{}$$

Also, F = mg

$$\Rightarrow \mathrm{}\mathrm{}\mathrm{g}=\mathrm{}\mathrm{G}\frac{\mathrm{}{\mathrm{M}}_{\mathrm{E}}}{{\mathrm{d}}^{2}}\mathrm{}$$

Where **M**_{E} is the mass of the earth, and **d** is the distance between the object and the center Earth.

- If the object is on or near the surface of the earth, then the distance d = R
_{E}, the radius of the earth.So, g = G $\frac{\mathrm{}{\mathrm{M}}_{\mathrm{E}}}{{{\mathrm{R}}_{\mathrm{E}}}^{2}}$

- Its value is given by 9.8 ms
^{-2}. - The earth is not a perfect sphere. As the radius of the earth increases from the poles to the equator, the value of g becomes greater at the poles than at the equator.

**Q. Calculate the Value of g**

Given,

Universal gravitation constant, G = 6.7 ×10^{–11c}N m^{2}kg^{-2},

Mass of the earth, M_{E} = 6 × 10^{24} kg,

Radius of the earth, R_{E} = 6.4 ×10^{6} m

**Motion of Objects under the Influence of Gravitational Force of the Earth**

Use the equations of motion, [with *a* = -g = -9.8 or -10 ms^{-2}]

Use,

$$\mathrm{v}\mathrm{}=\mathrm{}\mathrm{u}\mathrm{}-\mathrm{}\mathrm{g}\mathrm{t};\mathrm{}$$

$$\mathrm{s}\mathrm{}=\mathrm{}\mathrm{u}\mathrm{t}\mathrm{}\u2013\frac{1}{2}\mathrm{}\mathrm{g}{\mathrm{t}}^{2};\mathrm{}$$

$${\mathrm{v}}^{2}\mathrm{}=\mathrm{}{\mathrm{u}}^{2}\mathrm{}\u2013\mathrm{}2\mathrm{g}\mathrm{s}$$

**Mass**

Mass is a fundamental, universal property. The mass of an object is constant and does not change from place to place, symbol is **m**. SI unit is **kg**.

**Weight**

The weight of an object is the force with which it is attracted towards the earth.

Weight W = F_{g }=$\frac{\mathrm{G}{\mathrm{M}}_{\mathrm{E}}\mathrm{m}}{{{\mathrm{R}}_{\mathrm{E}}}^{2}}$ = mg

Where **M**_{E }is the mass and **R**_{E} is the radius of the Earth.

**Weight an Object on Moon**

Is approximately $\frac{1}{6}$^{th} of that on the Earth. Calculate.

Celestial body |
Mass(kg) |
Radius (m) |

Earth |
M |
R |

Moon |
M |
R |

**Thrust & Pressure**

- Thrust is the force acting on an object perpendicular to the surface of the object.
- Pressure is the force acting on unit area of a surface
$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{e}=\frac{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{u}\mathrm{s}\mathrm{t}}{\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}}$$

- The SI unit of pressure is N/m
^{2 }or N m-^{2}. It is called Pascal (Pa). - The same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area.
This is the reason why

- A nail has a pointed tip,
- Knives have sharp edges
- Buildings have wide foundations
- Bags have wide straps
- Camel is able to walk easily on the desert sand.

**Pressure in Fluids**

- Fluids exert pressure in all directions on the base and walls of the container in which they are enclosed.
- Pressure exerted in any confined mass of fluid is transmitted undiminished in all directions.

**Buoyancy**

When an object is immersed in a fluid it experiences an upward force called buoyant force. This property is called **buoyancy or upthrust**.

- Example, a completely empty closed bottle held under the water, bounces upwards when released.

**Density **

Mass per unit volume of an object is called its density

Density ρ = $\frac{\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{s}}{\mathrm{V}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}}$= $\frac{\mathrm{M}}{\mathrm{V}}$

The SI unit is kg/m^{3}

**Relative density**

The relative density of a substance is the ratio of the density of a substance to the density of water.

Relative density = $\frac{\mathrm{D}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}{\mathrm{D}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$

It is a ratio of similar quantities and has no unit.

**Why objects float or sink when placed on the surface of water?**

- If the density of an object is less than the density of a liquid, it will float on the liquid and if the density of an object is greater than the density of a liquid, it will sink in the liquid.
- Take some water in a beaker. Take a piece of cork and an iron nail of the same mass. Place them on the water. The cork floats and the nail sinks.

**Archimedes’ Principle**

Archimedes’ principle states that, when a body is partially or fully immersed in a fluid it experiences an upward force that is equal to the weight of the fluid displaced by it.

Archimedes’ principle has many applications. It is used in designing ships and submarines. Lactometers, which are used to determine the purity of a sample of milk and hydrometers for determining the density of liquids, are based on this principle.

**Apparent weight** = Weight in vacuum – Weight loss

= Weight in vacuum – Weight of fluid displaced