State universal law of gravitation and derive an expression for it. Explain its significance. Mass of an object is 20 kg. Find its weight on earth and on moon.
Answers
Explanation:
Gravitation
Universal Law of Gravitation
Every object in the universe has the property to attract every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (see the image given below).
Gravitational Force
F = force of attraction between two the objects ‘A’ & ‘B’
M = mass of ‘A’
m = mass of ‘B’
d2 = the square of the distance between ‘A’ & ‘B’
G = is the constant of proportionality and is known as the universal gravitation constant.
The SI unit of G is N m2 kg–2. It is obtained by substituting the units of force, distance and mass (as given in the following equation −
G=Fd2M×m
Henry Cavendish had calculated the value of ‘G’ as 6.673 × 10–11 N m2 kg–2.
Henry Cavendish had used a sensitive balance to find the value of ‘G.’
Significance of Universal Law of Gravitation
Following are the salient significance of the Universal Law of Gravitation −
It explains the force that binds all objects (including human beings) to the earth
It describes the motion of the moon around the earth
It explains the motion of planets around the Sun
It clarifies the tides due to the moon and the Sun
Free Fall
Whenever an object falls towards the earth, it involves an acceleration; this acceleration is produces due to the earth’s gravitational force.
Free Fall
The acceleration, produces due to the earth’s gravitational force, is known as the acceleration due to the gravitational force of the earth (or acceleration due to gravity).
The acceleration produces due to the gravitational force is denoted by g.
As the radius of the earth increases towards the equator (from the poles) the value of ‘g’ becomes greater at the poles than at the equator.
The Value of g
Value of g is calculated as −
g=GMR2
G = universal gravitational constant, which is = 6.7 × 10–11 N m2 kg-2
M = mass of the earth, which is = 6 × 1024 kg
R = radius of the earth, which is = 6.4 × 106 m
So,
g=6.7×10−11Nm2kg−2×6×1024kg(6.4×106m)2
$=9.8 \: m \: s^{-2}$
So, the value of acceleration due to gravity of the earth (g) is 9.8 m s-2
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