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Explain gravitational force by a suitable example.

Last updated date: 13th Jun 2024
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Hint: We can obtain the relationship of gravitational force with mass and radius and write its formula through which we can explain the universal constant of gravitation. Afterwards, we will apply Newton's third law of motion on the gravitational force and hence prove that two masses can apply force onto each other of equal magnitude.

Complete answer:
According to Newton's universal law of gravitation, “every particle in the universe attracts every other particle in the universe with a force which is directly proportional to the product of the two masses, and inversely proportional to the square of distance between them.” The direction of this force is along the line joining them. This force of attraction is called the gravitational force.

According to this law, the force of particle 1 with mass \[{m_1}\] on a particle 2, with mass\[{m_2}\]is given by the following formula:
\[{\vec F_{(12)}} = \dfrac{{G{m_1}{m_2}}}{{{{\vec r}_{(12)}}^2}}\] ,
Where, G is a constant and it is known as the universal constant of gravitation and \[{\vec r_{(12)}}\] is the distance between particle 1 and particle 2. G has the same value at all places in the universe and at all times. The value of G was first obtained by Cavendish and its value is $6.67 \times 10^{-11}$ \[\dfrac{{N{m^2}}}{{k{g^2}}}\]. The dimensional formula of G is\[[{M^{( - 1)}}{L^3}{T^{( - 2)}}]\]

According to Newton’s third law of motion, every action has an equal and opposite reaction. Hence the force of particle 2 on particle 1 will be as follows:
\[{\vec F_{(21)}} = - {\vec F_{(12)}} = - \dfrac{{G{m_1}{m_2}}}{{{{\vec r}_{(12)}}^2}}\]
Earth revolves around the Sun because of the gravitational force. Even though the distance between the Sun and earth is quite large, but so are the masses of the earth and the sun, hence the gravitational force is large enough to keep the earth around the sun in fixed orbits. The earth orbits because the earth’s velocity is perpendicular to the gravitational force, and hence there is the production of orbital motion.

Note: Gravitational force is the weakest of the four basic forces, and yet most of the universe around us sustains due to gravity. The other three forces include strong nuclear force, weak nuclear force and the electromagnetic force. Among these forces, a strong nuclear force is the strongest force existing in the universe.