Presence of gravitation or gravitational force was first brought up by Sir Isaac Newton. Story of falling of apple on Newton’s head is very much familiar. Apple fell on head of newton, on basis of this observation, he carried out experiments. Moreover, the experiments revealed the existence of gravitational force on basis of which universal law of gravitation was presented by Newton. Thus, theories of gravitation explains that each all object in universe are attracted by each other through the force called gravitational force.
The universal law of gravitation
The universal law of gravitation states that,
“Force between two bodies is directly proportional to product of masses and inversely proportional to square of distance between.”
Mathematical expression for law of gravitation
Consider two objects A and B, having masses M and m. Let d be the distance between the masses and F be the force of attraction.
By law of gravitation,
Also, Force is directly proportional to product of masses and inversely proportional to square of distance between them.
Therefore, F ∝ M × m
F ∝ 1/d2
Therefore we, get,
F ∝ M × m / d2
Therefore, F = G M m/ d2
G is constant of proportionality called Gravitational constant.
SI unit of Gravitational constant is Nm2 / kg2 and also its value is 6.673 × 10-11 Nm2 / kg2 .
Importance of gravitation
Body falling from height possess acceleration. In this case, acceleration is result of gravitational force exerted by earth on the body. This attracts the body towards the earth, thereby, allowing the freefall. Acceleration of object undergoing freefall is called acceleration due to gravity. It is positive if acceleration is in the direction of velocity and negative if acceleration is in opposite direction of velocity. Denoted by g and SI unit is m/s2.
Value of g is calculated with help of Gravitational law,
F = GMm/ d2
Therefore, mg = GMm /d2
Thus, g = G M/d2
If body is at earth’s surface then, g= GM / R2. Value of acceleration due to gravity is 9.8 m/s2. As earth is not exactly spherical, as a result, value of g is larger at poles than on equator.
Body undergoing freefall is independent of mass. If paper and stone is allowed to fall freely in vacuum, both reach at same time on the ground.
Keywords: Universal law of gravitation, Mathematical expression of law of gravitation, Significance of gravitation, Freefall, Importance of gravitation
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Where is the video for the topic Gravitation and universal law of gravitation?
Hi
you can watch video here,
https://learnfatafat.com/topic/10-01-introduction-gravitation/
or
https://www.youtube.com/watch?v=eP2iOedKppM