Question

state the universal law of gravitation and derive its expression​

Answer 1

Answer:

The Law of Universal Gravitation states that 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 centers.

Explanation:

Newton’s Law of Universal Gravitation

Newton went on to discover the law of gravitation. According to the Universal law of gravitation, the force between two bodies is directly proportional to their masses and inversely proportional to a square of the distance. Mathematically it can be 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

This constant of proportionality is known as Universal Gravitation Constant. With careful experiments, the value of gravitational constant was found to be 6.67 x 10−11 m3⋅kg−1⋅s−2N. This experiment was performed by Henry Cavendish. Also, the value of ‘G’ remains constant throughout the universe.

Answer 2

The universal law of gravitation:-

The Universal law of gravitation states that

The Universal law of gravitation states that Newton’s Law of Universal Gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

The universal gravitation equation thus takes the form :-

F∝m1m2/r2

F∝m1m2/r2 

⇒F=Gm1m2/r2

⇒F=Gm1m2/r2

$F= G\times \frac{\ m1 \times m2}{r {}^{2} }$

I will show you with the solved question

Calculate the gravitational force of attraction between the Earth and a 70 kg man standing at a sea level, a distance of 6.38 x 106 m from the earth’s centre.

Solution:

Given:

m1 is the mass of the Earth which is equal to 5.98 x 1024 kg

m2 is the mass of the man which is equal to 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=(6.673×10−11)(5.98×1024)(70)

(6.38×10−11)2=685NF=(6.673×10−11)(5.98×1024)(70)

(6.38×10−11)2=685N

F=685N