# Gravitation Notes for SSC and Railways

Gravity is one of the most important requirement of life in the Universe. Although no one thought about it until one day when Newton thought “why apples always fall straight to the ground”. The main contribution in this field comes from Newton and Kepler.

This topic is important for many competitive examination including JEE and NEET. Although for exams like SSC CGL and CHSL, not much numerical is involved.

# Gravity (Gravitation)

Gravity is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

## Universal Law of Gravitation

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

force ∝ m_{1}m_{2}and force ∝ 1 / r^{2}force ∝ m_{1}m_{2}/ r^{2}

**f = (Gm**

_{1}m_{2})/r^{2}(where **G** – Universal Gravitational Constant, **m _{1}**,

**m**are the masses of any two objects and r is the distance between the center of the objects)

_{2}- Value of G =
**6.67 x 10**was discovered by Henry Cavendish.^{-11} - SI Unit of G: Nm
^{2}kg^{-2}

### Free Fall

Object falling only because of gravitational force

**g = GM / R**

^{2}(where g – acceleration due to gravity, M – mass of earth and R – Radius of earth)

- g is independent on mass of the object
- g is constant near the earth, i.e., g =
**9.8 m/s** - Value of g at the centre of earth is
**0** - Earth is flattened at poles, thus radius of earth is less at poles than at equator. Hence the value of g is less at equator than at poles, also g is greater at North pole than South pole, thus
**g**._{North Pole}> g_{South Pole}> g_{Equator}

### Mass

The quantity which measures the inertia of a body.

- Scalar Quantity
- SI unit: kg
- Mass of a body can’t be 0.
- Irrespective of the position of the object in the universe, mass will always remain constant.
**Center of Mass**: The point where total mass of body is supposed to be concentrated.

### Weight

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

**w = m x g**

- Vector Quantity
- SI unit: N
- Weight of 1 kg mass is 9.8 N
- Weight of an object varies from place to place (because of change in the value of g)
- At the centre of earth, weight becomes zero (∵ g = 0)

### Actual Weight

The height felt by a body near the earth’s surface is called its actual weight.

### Apparent Weight / Effective Weight

The deviated value of weight of a body due to variation of g is known as its apparent weight.

### Weightlessness

When an object is under free fall, it is weightless and this phenomenon is known as weightlessness.

Weightlessness is achieved

- During free fall under gravity
- Inside a space craft or satellite
- At the centre of the earth
- When a body is lying in a free falling lift

### Apparent weight in a Lift

- When either the lift is stationary or moving with constant velocity: No change in weight.
- When lift is accelerating downwards: Weight will be less than actual weight.
- When lift is accelerating upwards: Weight will be more than actual weight.

### Weight of the body on the moon

As mass and radius of the moon are less than that of Earth, so the force of the gravity at the moon is also less than that of earth.

- Gravity on the moon is about 1.622 m/s
^{2} - g
_{moon}≈ 1/6 x g_{earth} - g
_{sun}≈ 27 x g_{earth}

The tides in the sea are primarily due to the gravitational effect of the Moon on the Earth.

### Pressure

The thrust on unit area is called pressure (SI unit: Pa)

Pressure = Thrust / Areawhere, Thrust = The force acting on an object perpendicular to the surface

### Buoyancy

The upward force exerted by the water on the bottle is known as upthrust or buoyancy

### Archimedes Principle

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.

### Relative Density

RD = Density of Substance / Density of water

### Planets

Heavenly bodies which revolves around the sun are called planets.

### Satellites(Natural, Artificial)

The heavenly bodies which revolves around the planet are called satellites.

### Important Artificial Satellites

#### 1. Geostationary Satellites

The satellites which appear to be at fixed position at a definite height to an observer on the earth, are called geostationary satellites.

Height above Surface of earth = 36000 km Radius of orbit = 42400 kmTime Period = 24 h

#### 2. Polar satellites

These are the satellites which revolve in polar orbits around the earth.

Height above surface of earth = 880 kmTime period = 84 min

NOTE: The geostationary environmental satellites are used for short range whereas polar satellites are used for longer term forecasting.

##### Uses/Applications of Artificial Satellites

- Weather Forecasting
- Studying upper region of atmosphere
- Study of cosmic rays and solar radiations
- To determine exact shape and dimensions of the earth
- Communicating through radio, TV, telephone, etc.

## Kepler’s law of planetary motion (By Johannes Kepler)

Kepler gave 3 laws regarding motion of planets around Sun.

### 1. First Law (Law of Orbits)

Planets revolve in an elliptical path around the Sun, the Sun being at one of the two foci of the ellipse.

### 2. Second Law (Law of Areas)

The radius vector of any planet relative to the Sun sweeps out equal area in equal time.

### 3. Third Law (Law of Periods)

The square of the period of revolution of any planet around the Sun is proportional to the cube of the semi-major axis of the elliptical orbit.

**T**

^{2}∝ a^{3}(where T – time period of revolution, a – semi-major axis)

### Orbital Velocity (V_{0})

Orbital Velocity of a satellite is the maximum velocity required to put the satellite into a given orbit around the earth.

**V**

_{0}= R√[g/(R_{e}+ h)](where R_{e} – radius of Earth, h – height of the satellite from Earth’s surface)

### Escape Velocity (V_{e})

The minimum speed with which a body needs to be projected vertically upwards from the surface of earth, so that it crosses the gravitational field of the earth and never returns on its own.

**V**

_{e}= √[2GM]/R(where R – Radius of planet/Earth)

- For Earth,
**V**_{e}= 11.2 km/s - If V
_{e}= V_{o}, then object will escape from its path

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