Mass and Weight Explained
MASS
 The mass of a body is the quantity of matter (or material) contained in it.
 Mass is a scalar quantity which has only magnitude but no direction.
 The mass of a body (or object) is commonly measured by an equal arm balance.
 The SI unit of mass is kilogram which is written in short form as kg.
A body contains the same quantity of matter wherever it be—whether on earth, moon or even in outer space.
 So, the mass of an object is the same everywhere.
 For example, if the mass of an object is 5 kilograms on the earth, then it will have the same mass of 5 kilograms even when it is taken to any other planet, or moon, or in outer space.
 Thus, the mass of a body (or object) is constant and does not change from place to place.
 Mass of a body is usually denoted by the small ‘m’.
 Mass of a body is a measure of inertia of the body and it is also known as inertial mass.
 The mass of a body cannot be zero.
WEIGHT
 The earth attracts everybody (or object) towards its centre with a certain force which depends on the mass of the body and the acceleration due to gravity at that place.
 The weight of a body is the force with which it 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.
 We know that, Force = mass × acceleration
 The acceleration produced by the force of attraction of the earth is known as acceleration due to gravity and written as ‘g’.
 Thus, the downward force acting on a body of mass ‘m’ is given by :
Force = mass × acceleration due to gravity
or Force = m × g
ACCELERATION DUE TO GRAVITY
 When an object is dropped from some height, its velocity increases at a constant rate.
 In other words, 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 and it is denoted by the letter g.
 When a body is dropped freely, it falls with an acceleration of 9.8 m/s^{2} and when a body is thrown vertically upwards, it undergoes a retardation of 9.8 m/s^{2}.
 So, the velocity of a body thrown vertically upwards will decrease at the rate of 9.8 m/s^{2}.
 The velocity decreases until it reaches zero. The body then falls back to the earth like any other body dropped from that height.
Variation of gravity at different planets and space
 Gravity is a fundamental force of physics, one which we Earthlings tend to take for granted. You can’t really blame us.
 Having evolved over the course of billions of years in Earth’s environment, we are used to living with the pull of a steady 1 g (or 9.8 m/s^{2}). However, for those who have gone into space or set foot on the Moon, gravity is a very tenuous and precious thing.
 Basically, gravity is dependent on mass, where all things – from stars, planets, and galaxies to light and subatomic particles – are attracted to one another.
 Depending on the size, mass, and density of the object, the gravitational force it exerts varies.
 And when it comes to the planets of our solar system, which vary in size and mass, the strength of gravity on their surfaces varies considerably.
 For example, Earth’s gravity, as already noted, is equivalent to 9.80665 m/s^{2} (or 32.174 ft/s^{2}).
 This means that an object if held above the ground and let go, will accelerate towards the surface at a speed of about 9.8 meters for every second of free fall.
 This is the standard for measuring gravity on other planets, which is also expressed as a single g.
 In accordance with Isaac Newton’s law of universal gravitation, the gravitational attraction between two bodies can be expressed mathematically as F = G (m^{1}m^{2}/r^{2}) – where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant (6.674×10^{11} N m^{2}/kg^{2} ).
Variation of “g” as height increases.
 Please note that the value of acceleration due to gravity, g, is not constant at all the places on the surface of the earth.
 This is due to the fact that the earth is not a perfect sphere, so the value of its radius R is not the same at all the places on its Surface.
 In other words, due to the flattening of the earth at the poles, all the places on its surface are not at the same distance from its center and so the value of g varies with latitude.
 Since the radius of the earth at the poles is minimum, the value of g is maximum at the poles.
 Again, the radius of the earth is maximum at the equator,
 so the value of g is minimum at the equator (because radius occurs in the denominator of the formula for g).
 We find that the value of g is inversely proportional to the square of the distance from the center of the earth.
 Now, as we go up from the surface of the earth, the distance from the center of the earth increases, and hence the value of g decreases (because R increases in this case).
 The value of acceleration due to gravity, g, at an altitude of 200 km above the surface of the earth is 9.23 m/s^{2}
 At an altitude of 1000 km, g is 7.34 m/s^{2}
 At 5,000 km above earth g is 3.08 m/s^{2.}
 At 10,000 km g is 1.49 m/s^{2}
 At 20,000 km, g is 0.57 m/s^{2}
 Whereas at a height of 30,000 km above the surface of the earth, the value of g is only 0.30 m/s2.
