Gravitation and it's laws | Science Olympiad Class 9 PDF Download

What is Gravitation?

It was Sir Isaac Newton who first gave the term gravitation when he saw an apple falling from a tree and thought that ‘why an apple fall towards the earth and not going upward.’ Later, he realized that it is because earth attracts every object towards itself with a force called the gravitation force.

Universal Law of Gravitation

According to this law,

‘Every body in the universe attracts every other body with a force which is directly proportional

to the product of their masses and inversely proportional to the square of distance between them.’

F =G{(m₁×m₂)/r²)}

Where, G is constant known as ‘universal gravitational constant.’ Newton’s law of gravitation is universal because it is applicable to all the bodies having mass; whether the bodies are big or small, terrestrial or celestial such as star, planets, rocket etc.

Gravitational Constant, G

F =G{(m₁×m₂)/r²)}

⇒G=F ×{r² /(m₁+m₂)}

If m₁ = m₂= 1 kg and r = 1 m, F = G

Thus, the gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit mass kept at a distance of 1 meter from each other. The value of G has been found to be 6.67 × 10^–11 Nm²/kg². The force of gravitation is a vector quantity and it acts along the line joining the centers of mass of the two bodies. SI unit is Nm² kg^–2. The value of G does not depend on the medium between the two bodies, mass or distance between the two bodies.

Applications of Law of Gravitation

• Force of gravitation binds us with earth.
• The motion of moon around the earth is due to the gravitational force.
• It also helps the planets to revolve around the sun.
• Regular eruption of tides in the ocean and sea is due to gravitational force.

Acceleration Due to Gravity g

When an object is dropped from some height, a uniform acceleration is produced in it by the gravitational pull of the earth, and this acceleration does not depend on the mass of the falling object. ‘The uniform acceleration produced in a freely falling body due to the gravitational force of the earth is known as acceleration due to gravity.’ It is denoted by g and has value 9.8 m/s². When a body is dropped freely, it falls with acceleration of 9.8 m/s² and when a body is thrown vertically upwards, it undergoes a retardation of 9.8 m/s².

The force between ball of mass m and the earth of mass Me, is given by

F=G (mMe/Re²)   -- (i), Re = radius of the earth.

The force due to earth’s gravity is given by’

F = ma = mg – (ii) ( g = gravity )

Equating equations (i) and (ii) , we get

Mg = mMe/R_e² 

⇒g =G(M_e/R_e²)

G = 6.7 × 10^–11 Nm²/ kg², Me = 6 × 10²⁴kg, Re = 6.4 × 106m

Putting, these value, we get g = 9.8 m/s² 

  View Answer

Equations of motion of body falling freely under gravity

For freely falling bodies, the acceleration due to gravity is g. the horizontal distance of the freely falling bodies is known as height h, the three equations of motion are

v = u + gt

h = ut +(1/2) gt²

v² = u²+ 2gh

• When a body is falling vertically downward, its velocity is increasing, so the acceleration due to gravity, g is taken as positive.
• When a body is thrown vertically upwards its velocity is decreasing so the acceleration due to

  gravity g is taken as negative.

• When a body is dropped freely from a height, u = zero.

• When a body is thrown. vertically upwards, its final velocity, v = zero.

• The time taken by a body to rise to the highest point is equal to the time it takes to fall from the  same height,

Mass and Weight

Mass of a body is the total quantity of the matter contained in it. It is a scalar quantity which has only magnitude but no direction. The SI unit of mass is kilogram (kg). Mass of an object is same everywhere, whether on earth or on moon or in space.

The weight of a body is defined as the force with which a body is attracted towards the centre of the earth. In other words, the force of earth’s gravity acting on a body is known as its weight. Thus,

w = force = m × g

Since, g is constant everywhere, therefore at a given place W ∝ m, i.e, weight of a body is directly

proportional to its mass.

Thus, the weight of 1 kg mass is 9.8 Newtons. Weight is a vector quantity having downward

direction.

In space, force of gravity, g = 0 thus all the bodies feel weightlessness. Thus, the weight of a body

in space is zero.

  View Answer

Weight of the Object on Moon

Let M_m be the mass of the moon, and R_M be the radius of the moon. Let us consider an object of mass ‘m’ placed on the surface of the moon. Then the weight of the object on the surface is given by,

W_m = g(M_m×m )/R_m²_.....(i)

_{Weight of the same object on the surface of the earth is given by}

W_e = g(M_e×M )/R_e²_.....(ii)

W_m/W_e =(M_m/M_e) × (R_e²  ×R_m²)

Mass of earth, M_e = 6 × 10²⁴ kg

Mass of moon, M_m = 7.4 × 10²² kg

Radius of earth, R_e= 6400 km

Radius of moon, R_m = 1740 km

Putting these values in the ratio, we get,

W_m/W_e =1/6

Thus, weight of an object on the moon is one–sixth of its weight on the earth.

State Kepler’s Laws of Planetary Motion.

Johannes Kepler established three laws which defined the motion of planets around the sun.

1. First Law: Kepler’s first law states that the planets move in elliptical orbits around the sun, with the sun at one of the two foci of the elliptical orbit.
2. Second Law: Kepler’s second law states that each planet moves around the sun in such a way that the line joining the planet to the sun sweeps over equal areas in equal intervals of time. It means that a planet moves faster when it is closer to the sun, and it moves slowly when it is farther from the sun.                                                                                                                                                         Area ABC = Area A′ B′ C, covered in equal time intervals.
3. Third Law: Kepler’s third law states that ‘ the cube of the meandistance of a planet from the  sun is directly proportional to the square of time it takes to move around the sun’. 

             r³ ∝ T²    

Let A and B be the two planets whose time period are T₁ and T₂ .If r₁ and r₂ be their distance from the sun, then

T₁²/T₂²=r₁³/r₂³

Thrust and Pressure 

Thrust is the force acting on the body perpendicular to the surface. Its unit is same as that of force.

When you apply a force on the head of the drawing pin to enable it to get insert in the board, you are applying thrust on the pin. SI unit of thrust is Newton. Pressure is the thrust (force) applied normal to the surface per unit area. It is given by

P = Force/Area =F/A

The unit of pressure is N/m² or pascal. 1 Pa = 1 N/m². Thus, the effect of a force depends on the area of the object on which it acts. The same force can produce different pressures depending on the area over which it acts. Force applied on a smaller surface area produces larger pressure as compared to the same force applied to a larger surface area.

Applications of pressure