GRAVITATION

IMPORTANT TERMS

Gravitation: - Every object in the universe attracts other object by a force of attraction called gravitation.

Free fall: - When an object falls from a height under the influence of gravitational force only, it is known as free fall.

Mass: - The total content of an object is called mass. It remains constant throughout the universe.

Weight: - It is the force exerted on the body due to gravity.

Thrust: - Thrust is a kind of force applied on the object in a direction perpendicular to the surface.

Up-thrust: - It is a force (buoyant force) exerted on the object by a fluid in upward direction when immersed into it.

Pressure: - Thrust or force per unit area is called pressure.

Buoyancy: - Buoyancy is the ability of an object to float in a fluid.

Gravitational Constant: - It is a universal constant that is equal to 6.673X10-11 Nm2/Kg2.

Relative density: - Relative density is the ratio of the density of a substance to the density of a given reference (Standard) material.

Universal Law of Gravitation

Newton’s law of universal gravitation states that every object attracts every other object in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Let ‘F’ is the force of attraction between two objects of masses M and m which lies at a distance of ‘d’ from each other, then according to universal law of gravitation

F ∝ Mm/d2

F = G. (Mm/d2), Where ‘G’ is universal gravitational constant.

 

Gravitational constant (G)

• The value of G was found out by Henry Cavendish.
• The SI unit of G is Nm2kg−2. Its value is 6.673×10−11Nm2 kg-2.
• This Law is applicable to all objects present in the universe.
  • This law explains the cause of (i) revolution of moon around earth (ii) revolution of   planets around sun and (iii) causing of tides due to moon and sun.

Free Fall

It is a downward motion of a body where gravity is the only force acting upon it. In this case no change of direction takes place but the magnitude of velocity changes because of acceleration. This acceleration acts because of the force of gravitation and is denoted by ‘g’. This is called acceleration due to gravity. The unit of ‘g’ is ms–2 which is the same as that of acceleration.

Expression for Acceleration due to Gravitation ‘g’

Let ‘m’ is mass of the object under free fall and ‘g is acceleration due to gravity.  Therefore the magnitude of the gravitational force ‘F’ will be equal to the product of mass and acceleration due to the gravitational force.

             F= m X g ---------(i)

Now, according to Universal Law of gravitation,

F = G. (Mm/d2)---------(ii)

Thus, from above two expressions, we get,

            m X g=G. (Mm/d2)

or, g= G. (Mm/d2)---------(iii)

Where ‘M’ is the mass of the earth, and d is the distance between the object and the earth. Suppose an object is on or near the surface of the earth then‘d=R’, where ‘R’ is the radius of earth.

Thus for objects for on or near the surface of earth,

                    g= G. (Mm/R2) ---------(iv).

Putting the value of G = 6.673×10−11Nm2 kg-2, Mass of earth = 6 X1024 kg, and Radius of earth, R= 6.4 X 1024 m, in equation (iv), we get g= 9.8 ms-2.

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

All the equations for the uniformly accelerated motion of objects is valid for motion of objects under the influence of gravitational force of the earth with acceleration ‘a’ replaced by ‘g’. Therefore these equations are:

v= u + gt;

s= ut + gt2/2;

v2= u2 + 2gs.

Where ‘u’ and ‘v’ are the initial and final velocities and ‘s’ is the distance covered in time ‘t’.

Mass

• The mass of an object is the measure of its inertia.
• Mass of an object remains the same throughout the universe. Thus, the mass of an object is constant and does not change from place to place.
• The SI unit of mass is kilogram (kg).

 

Weight

• The weight of an object (W) is the force with which it is attracted towards the earth.
• The SI unit of weight is the Newton (N), same as that of force.
• W= m X g, Where ‘m’ is mass of object and ‘g’ is acceleration due to gravity.
• The weight of an object on the moon is the force with which the moon attracts that object.
• Weight of the object on the moon = Weight of that object on the earth/6.

Thrust and Pressure

·       Force exerted by an object perpendicular to the surface is called thrust.

·       Force exerted by any object per unit area is called pressure.

·       Pressure=Thrust/Area or, (Pressure= F/A)

·       SI unit of thrust is the Newton (N), same as that of force.

·       SI unit of pressure is Nm-2 where 1Nm-2 = 1 Pascal.

 

Thrust and pressure in everyday life

·     Pressure exerted by a brick: A stretched brick kept on the ground exerts less pressure than a brick kept on the ground in standing position due to the surface area of contact of brick in stretched position is more in comparison to the brick in standing position.

·     Tractor has broader tyres: Tractor is made mainly for agriculture purpose because of its broader tyres. Thus a tractor can easily run over the muddy field due to less pressure exertion over the ground as pressure decreases with increase in surface area or contact.

·     One end of a nail is pointed: A nail is pushed from pointed side in a wall or wood because nail exerts more pressure through pointed side over the wall or wood.

·     The straps of school bag are broader: School bags with broader straps exert less pressure over the shoulder while being carried over the shoulder and thus a student feels easy to carry even a heavy bag with more books.

 

Pressure in Fluids

Gas and liquid are considered as fluids. Like solid objects, fluids also have weight and thus exert pressure in all direction over the inner wall of container in which they are kept.

 

Buoyancy and Up-thrust

The property of buoyancy exists in liquid due to which an object floats in it. The buoyant force or up thrust is the upward force exerted by fluids over the surface of contact of an object which is immersed in fluids. If the force exerted by the object is greater than the upward thrust by water, the object will sink in water otherwise it floats over water.

Buoyancy Factors

·     Volume of the object: Up thrust exerted by a fluid increases with the volume of object immersed in it.

·     Density of fluid: Denser liquid exert more up thrust because upthrust increases as increase of density of fluid.

Density

·       Mass per unit volume of an object is called density.

·       The SI unit of density is kgm-3.

Relative density

·     Relative density is a ratio of the density of a substance to the density of a given reference material.

·     Relative density has only numeric value. It has no unit because it is a ratio of two similar physical quantities.

·     Usually water is used as reference material.

·     The relative density of an object decides the buoyancy of object in the liquid. If an object has relative density greater than 1 then the object is denser than water and therefore it will sink in water.

 Archimedes’ principle

It states that the upward force (buoyant force) that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid displaced by it and acts in the upward direction at the center of mass of the displaced fluid.

Application of Archimedes’ principle

Submarine floats by reducing water in its ballast tank and thus its weight becomes lesser than the buoyant force. Similarly it submerges by letting water in the ballast tank so that its weight becomes greater than the buoyant forces.

Ship floats on the surface of water because the volume of water displaced by the ship is enough to have an up-thrust equal to the weight of the ship.

Hydrometer is used to measure the relative density of liquids. It floats higher in a liquid of higher density.

Hot air balloon rises and floats due to buoyant force. It starts descending if its weight is more than the buoyant force.

INTERESTING FACTS

• ‘G’ stands for Newton's universal gravitational constant, whereas ‘g’ stands for the acceleration due to gravity at a certain point.
• All objects falls over the earth with the same rate because the value of ‘g’ does not depend upon its mass or its distance from the earth.
• The value of ‘g’ is considered as positive when object moves towards the earth and it is considered as negative when object is thrown upward.
• The value of ‘g’ varies on the surface of the earth, decreasing from poles to the equator
• In honour of scientist Blaise Pascal, the SI unit of pressure is called Pascal, denoted as Pa.
• The downward force acting on the nail is greater than the up-thrust of water on the nail and thus it sinks.