define universal law of gravitation and derive mathematically
Answers
Answer:
Gravitation, also known as gravity, is a force that exists among all material objects in the universe. Gravity acts on objects of all sizes ranging from subatomic particles to cluster of galaxies. Sir Issac Newton studied its behaviour with his famous law of gravitation. In physics, gravitation is defined as the force that attracts every object to the centre of gravity. In general, gravitation is the force exerted by the body due to the virtue of its mass.
The Universal Law of Gravitation states:
“Every object of mass in the Universe attracts every other object of mass with a force which is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centres.”
In this article, let us learn more about the universal law of gravitation.
Newton’s Law of Universal Gravitation
According to the Universal law of gravitation, the force between two bodies is directly proportional to their masses and inversely proportional to the square of the distance between them. Mathematically, it is represented as follows:
F∝m1m2r2 ⇒F=Gm1m2r2
where,
F is the gravitational force between two bodies
m1 is the mass of one object
m2 is the mass of the second object
r is the distance between the centers of two objects
G is the Universal Gravitation Constant.
Henry Cavendish, with careful experiments, found the value of Gravitational Constant to be 6.67 x 10−11 m3⋅kg−1⋅s−2N. The value of ‘G’ remains constant throughout the universe.
Weight and the Gravitational Force
In the law of gravity, we noticed that the mass is a crucial quantity. We consider mass and weight to be the same, but in reality, they are related but are different. Weight is the gravitational force exerted on an object of a certain mass. The weight of an object can be obtained by multiplying the mass m of the object by the acceleration due to gravity, g, at the surface of the Earth. The measured gravitational acceleration at the Earth’s surface is found to be about 980 cm/second/second.
The measure of how much material is in an object is known as mass, while weight is the measure of the gravitational force exerted on the material in a gravitational field; thus, mass and weight are proportional to each other, with the acceleration due to gravity as the proportionality constant. It is observed that the mass is constant for a given object, but the weight depends on the location of the object. To better understand, let us consider the following example, say we transported an object of mass m to the surface of Neptune, the gravitational acceleration would change because the radius and mass of the Neptune both differ from those of the Earth. Thus, our object has mass m both on the surface of the Earth and on the surface of the Neptune, but it will weigh much more on the surface of Neptune because the gravitational acceleration there is 11.15 m/s2.
Solved Problem
Question:Calculate the gravitational force of attraction between the Earth and a 70kg man if he is standing at a sea level, a distance of 6.38 x 106 m from the earth’s center
Answer:
Given:
m1 is the mass of the Earth which is equal to 5.98 x 1024 kg
m2 is = 70 kg
d = 6.38 x 106 m
The value of G = 6.673 x 10-11 N m2/kg2
Now substituting the values in the Gravitational force formula, we get
F=(6.673×10−11Nm2/kg2).(5.98×1024kg).(70kg)(6.38×106m)2
F=686N
Explanation:
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Answer:
F= G (m1 m2) / R2
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