Chapter GRAVITATION WORK, POWER AND ENERGY Physics Study 1st Year Karachi Board And Punjab Board - FULL NOTES

Physics..1st Year..Chapter 2

GRAVITATION

Gravitation:::

The property of all objects in the universe which carry mass, by
virtue of which they attract one another, is called Gravitation.
Centripetal Acceleration of the Moon
Newton, after determining the centripetal acceleration of the moon,
formulated the law of universal gravitation.
Suppose that the moon is orbiting around the earth in a circular orbit.
If V = velocity of the moon in its orbit,
Rm = distance between the centres of earth and moon,
T = time taken by the moon to complete one revolution around the earth.
For determining the centripetal acceleration of the moon,. Newton
applied Huygen's formula which is
a(c) = v2 / r
For moon, am = v2 / Rm ..................... (1)
But v = s/t = circumference / time period = 2πRm/T
Therefore,
v2 = 4π2Rm2 / T2
Therefore,
=> a(m) = (4π2Rm2/T2) x (1/Rm)
a(m) = 4π2Rm / T2
Put Rm = 3.84 x 10(8) m
T = 2.36 x 10(6) sec
Therefore,
a(m) = 2.72 x 10(-3) m/s2
Comparison Between 'am' AND 'g'
Newton compared the centripetal acceleration of the moon 'am' with
the gravitational acceleration 'g'.
i.e., am / g = 1 / (60)2 ................. (1)
If Re = radius of the earth, he found that
Re2 / Rm2 - 1 / (60)2 ......................... (2)
Comparing (1) and (2),
am / g = Re2 / Rm2 ..................................... (3)
From equation (3), Newton concluded that at any point gravitational
acceleration is inversely to the square of the distance of that point
from the centre of the earth. It is true of all bodies in the
universe. This conclusion provided the basis for the Newton' Law of
Universal Gravitation.