Question

How to calculate the force of gravitational attraction between a person (\[mass = 75kg\]) and earth (\[mass = 5.98 \times {10^{24}}Kg\] and mean radius \[6.37 \times {10^6}m\])?

Answer 1

Hint: To solve this numerical we need to know Newton’s law of gravitation. Newton’s law of gravitation states that- “Every object in the universe attracts every other object towards itself with a force which is directly proportional to the product of their masses and inversely population to the square of distances between their centers”.

Complete step by step answer:
The formula used for this numerical as per the law is-
$F = \dfrac{{G({m_1}{m_2})}}{{{r^2}}}$
Where
\[F = \] the gravitational force of attraction (whose value is unknown)
\[G = \] gravitational constant= \[6.67 \times {10^{ - 11}}N{m^2}/k{g^2}\]
\[{m_2}\]= mass of person = \[75kg\]
\[{m_1}\]= mass of earth= \[5.98 \times {10^{24}}kg\]
\[r = \] distance from the center of the earth and the center of person=\[6.37 \times 10\Lambda 6\] m
Substituting the values in the formula, we get
\[F = \dfrac{{6.67 \times {{10}^{ - 11}} \times 5.98 \times {{10}^{24}} \times 75}}{{6.37 \times {{10}^6}}}\]
\[F = 737.24N\] (after calculation)
Therefore, the force of gravitational attraction between the person and the earth is calculated to be \[737.24N\].
Since the gravitational force is directly proportional to the product of their masses. Therefore, the heavier the body's will be the gravitational force or pull, and the lesser the mass, the lesser will be the gravitational pull or force.
Gravitational force is inversely proportional to the square of the distance between centers of two bodies, therefore greater the distance lesser will be the gravitational force between the two bodies and vice-versa.
Sir Isaac Newton discovered gravity. Every object having mass will attract every other body towards itself and therefore every object gets attracted towards the earth and even in space all, the celestial bodies are attracted towards each other by the effect of gravity.

Note: Therefore, by substituting the given values in the formula we know that the value of the gravitational force of attraction is \[ 737.24N\] i.e. a gravitational force of \[737.24N\] must be applied to the two bodies to keep them at a distance of \[6.37 \times {10^6}\] meter.
For solving numerical on gravity, we should keep in mind certain points-
Must be well versed with the laws and theories, noting down the given values, known values and which is to be found out, and the formulae should be kept in mind.