Gravitation

Summary

(1) All objects fall on the ground if dropped from a height.

(2) When an object is thrown upward, it comes to the ground after reaching a certain height.

(3) Earth attracts all the objects towards it.

(4) The force of attraction by which earth attracts all object towards it is called GRAVITY or GRAVITATION or FORCE OF GRAVITATION.

(5) Sir Isaac Newton an English scientist gave the Theory of Gravitation.

(6) Moon revolves round the earth because of gravitational pull of earth.

(7) In similar way, all planets revolve round the sun because of gravitational pull of SUN.

(8) Every object in the universe attracts every other object.

(9) Aristotle first of all gave the philosophy of gravitation after many experiments.

(10) Newton's Law of Gravitation states "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".

(11) The force acting upon the objects is along the line joining the centres of two objects

(12) Mathematical formulation of Newton?s Law of Gravitation `F=G(Mxxm)/d^2`

(13) Where, G is constant of proportionality and called Universal Gravitational Constant. The value of Gravitational constant, G does not depend upon the medium between the two bodies and also does not depend on the distance or masses of the bodies.

(14) The force of attraction, F between objects is called Gravitational Force or Force of Gravitation.

(15) SI unit of G is N m² kg ^–2

(16) The Gravitational constant G is numerically equal to the Force of Gravitation between two bodies of unit masses kept at a unit distance from each other. That means G = F.

(17) The accepted value of G is 6.673 × 10 ^–11 N m² kg ^–2

(18) Inverse Square Rule of Newton: Every object in the universe attracts every other object with a force which is inversely proportional to the square of the distance between them.

(19) According to the Inverse Square Rule, the gravitation force decreases with the increase in distance between objects.

(20) When an object falls from a height on its own; and no force other than gravitation is applied on the object, then it is called free fall and object is called free falling object.

(21) Acceleration due to Gravity (g) = 9.8 m s^–2

(22) The acceleration because of gravity for any object does not depend upon the mass of object.

(23) The acceleration due to gravity at moon, g = 1.63 m s ^–2

(24) Mass is the quantity of matter contained in an object.

(25) Mass is denoted by the small letter 'm'.

(26) Weight of an object is a quantity because of the force of gravitation.

(27) Weight is denoted usually by 'W'

(28) Weight = Mass × acceleration due to gravity or W = m × g

(29) SI unit of weight = Newton (N)

(30) The weight of an object is `1/6th` on the moon than on the earth.

(31) The net force, which is acted in a particular direction, is called thrust.

(32) The SI unit of thrust is N.

(33) The force per unit area acting on an object concerned is called pressure.

(34) The SI unit of pressure is pascal (Pa) = N m^–2

(35) Pressure `={text(Thrust)}/{text(Area)}`

(35) Liquids and gases exert pressure due to their weights.

(36) An upward force exerted by liquid or gas that opposes the weight of an immersed object is called buoyancy.

(37) The buoyancy is also known as buoyant force.

(38) Buoyant force is actually upward thrust due to liquid.

(39) The mass per unit volume of a material is called density or the mass density of the material.

(40) Density is denoted most often by the symbol `rho` and it is read as "rho".

(41) density`\ rho = {text(Mass)}/{text(Volume)}`

(42) SI unit of density `=kg\ m^(-3)`

(43) Archimedes' Principle states that when an object (solid) is immersed in water partially or fully, it experiences a loss in its weight because of the buoyant force of water, which is equal to the weight of the liquid displaced by the object.

(44) If the density of the object is less than the liquid then the object will float in that liquid, otherwise the object will sink.

(45) Relative Density is the ratio of a substance to the density of given materials.

(46) Relative Density is also known as Specific Gravity.

(47) Specific Gravity is the ratio of density of a substance to the density of water.

(48) Relative Density `={text(Density of substance)}/{text(Density of water)}`

(49) Since, relative density is the ratio of two densities, thus Relative Density has no unit.

NCERT In Text Questions and Answers

Question (1) State the universal law of gravitation.

Answer:

Universal Law of Gravitation states that 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.

Question (2) Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

Answer:

Formula to find the magnitude of gravitational force,

`F=G(M\ m)/d^2`

Where,

M is the mass of earth

m is the mass of object on the surface of earth

d is the distance between earth and object

F is the gravitational force

G is the gravitational constant.

Question (3) What do you mean by free fall?

Answer:

When an object falls from a height on its own; and no force other than gravitation is applied on the object, then it is called free fall and object is called free falling object. For example when a piece of stone is dropped from a height, it is called free falling object.

Question (4) What do you mean by acceleration due to gravity?

Answer:

When an object falls towards earth; its velocity changes with a constant rate. The rate of change of velocity does not depend upon the mass of the object.

This means rate of change of velocity, i.e. acceleration does not depend upon the mass of the object. And this acceleration is called acceleration due to gravity.

Acceleration due to gravity is 9.8 m s^–2 of a free falling object.

Question (5) What are the differences between the mass of an object and its weight?

Answer:

Question (6) Why is the weight of an object on the moon `1/6\ th` its weight on the earth?

Answer:

We know that the weight of an object is the product of its mass and acceleration due to gravity.

This means

Weight = mass × acceleration due to gravity.

The mass of an object remains constant everywhere.

The acceleration due to gravity on earth is equal to 9.8 m s^–2 and on moon is 1.63 m s^–2.

The acceleration due to gravity on the moon is about 6 times smaller than the acceleration due to gravity on earth.

Therefore, the weight of an object on the moon is `1/6\ th` of the weight on the earth.

Question (7) Why is it difficult to hold a school bag having a strap made of a thin and strong string?

Answer:

This happens because of pressure.

Pressure is the force acting on a unit area of the object.

Pressure increases with decrease in area. That is, if area of the objet decreases the pressure increases on the other hand if area of the object increases pressure decreases.

This is the cause that usually school bags have broader straps. Because of broader straps, pressure diverted to a large area and hence made easier to carry the bag.

On the other hand in the case of thin straps, pressure exerted to smaller area and hence increases.

And hence, it is difficult to hold a school bag having a strap made of a thin and strong string.

Question (8) What do you mean by buoyancy?

Answer:

When an object is immersed in water there are two forces act on this.

First; gravitational force of earth pulls the object downwards while pressure exerted by water pushes the object upwards. This upward force exerted by water or other liquid that pushes the object upward is called buoyancy.

An upward force exerted by liquid or gas that opposes the weight of an immersed object is called buoyancy.

Question (9) Why does an object float or sink when placed on the surface of water?

Answer:

The sinking or floating of an object in a liquid depends upon the density of liquid and object.

If the density of the object is lesser than the density of the liquid, then object floats in that liquid. And if the density of the object is greater than the density of the liquid, then object sinks in that liquid when placed on the surface of water.

Example: The density of a cork is less than that of water and hence cork float on the surface of water.

While the density of an iron nail is more than that of water, and hence nail sinks when placed on the surface of water.

Thus, because of difference in density an object float or sink when placed on the surface of water.

Question (10) You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?

Answer:

Air is also a liquid and it exerts an upward thrust that is buoyant force. Thus, while weighing due to buoyant force exerted by air we get slightly less value than that of actual one.

Thus, if one find his mass to be 42 kg on a weighing machine, thus this mass is less than that of actual.

Thus, mass is slightly more than that 42 kg.

Question (11) You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?

Solution:

A weighing machine indicates the weight because of gravitational pull of the object. There is air in our surroundings which also exerts the buoyant force over the objects. Buoyant force exerted by a fluid increases with increase in volume of an object.

The volume of the cotton bag is more than the iron bar hence buoyant force exerted on the cotton bag is more than the iron bar. Because of the more buoyant force exerted by the air on the cotton bag, it appears lighter and hence weighed less than its actual weight.

Therefore, cotton bag is heavier one.