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## Gravitation

Every body attracts other body by a force called force of gravitation

__Newton’s law of Gravitation__

The force of gravitational attraction between two point bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Consider two point bodies of mass *m* and *n* placed at a distance *r*. The force of gravitation attraction between them, **F = Gm ^{2}n^{2}/r^{2}**.

Here,

**G**is constant called universal gravitational constant. The value of G is 6.67 x 10

^{-11}Nm

^{2}/kg

^{2}.

» Gravity The gravitational force of earth is called gravity i.e. gravity is the force by which earth pulls a body towards its centre.

The acceleration produced in a body due to force of gravity is called acceleration due to gravity (denoted as g) and its value is 9.8 m/s

^{2}.

» Acceleration due to gravity is independent of shape, size and mass of the body.

## Varition in g

1. Value of g decrease with height or depth from the earth surface.

2. g is maximum at pole.

3. g is minimum at equator.

4. g decreases due to rotation of earth.

5. g decrease if angular speed of earth increases and increases and increases if angular speed of earth decreases.

6. If angular speed of earth become 17 times its present value, a body on the equator become weightless.

## Weight of a body in a lift

1. If lift is stationary or moving with uniform speed (either upward or down ward), the apparent weight of a body is equal to its true weight.

2. If lift is going up with acceleration, the apparent weight of a body is more than the true weight.

3. If lift is going down with acceleration, the apparent weight of a body is less than the true weight.

4. If the cord of the lift is broken, it falls freely. In this situation the weight of a body in the lift becomes zero. This is the situation of weight lessness.

5. While going down, if the acceleration of lift is more than acceleration due to gravity, a body in the lift goes in contact of the ceiling of lift.

## Kepler's Laws of planetary motion

1. All planets move around the sun in elliptical orbits, with the sun being at rest at one focus of the orbit.

2. The position vector of the planet with sun at the origin sweeps out equal area in equal lime i.e. The areal velocity of planet around the sun always remains constant.

A consequence of this law is that the speed of planet increases when the planet is closer to the sun and decreases, when the planet is far away from sun.

Speed of a planet is maximum when it is at perigee and minimum when it is at apogee.

3. The square of the period of revolution of a planet around the sun is directly proportional to the cube of mean distance of planet from the sun.

If T is period of revolution and r is the mean distance of planet from sun then T^{2} ∝ r^{3}

Clearly distant planets have larger period of revolution. The time period of nearest planet Mercury is 88 days where as time period of farthest planet Pluto is 247.7 years.