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(iv) the tides due to the moon and the Sun.
INTEXT QUESTIONS PAGE NO. 134
1. State the universal law of gravitation
Ans. The universal law of gravitation states that every object in the universe attracts every other object with a force called the gravitational force. The force acting between two
objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For two objects of masses m1 and m2 and
the distance between them r, the force (F) of attraction acting between them is given by the universal law of gravitation as:
F = Gm1m2 /r2
Where, G is the universal gravitation constant given by: G = 6.67x10-11Nm2 / kg2
2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Ans. Let ME be the mass of the Earth and m be the mass of an object on its surface. If R is the radius of the Earth, then according to the universal law of gravitation, the gravitational
force (F) acting between the Earth and the object is given by the relation:
F = Gm1m2 /r2
FREE FALL
When an object falls from any height under the influence of gravitational force only, it is known as free fall. In the case of free fall no change of direction takes place but the magnitude
of velocity changes because of acceleration.
This acceleration acts because of the force of gravitation and is denoted by ‘g’. This is called acceleration due to gravity.
EXPRESSION FOR ACCELERATION DUE TO GRAVITATION ‘G’.
Let mass of the object put under free fall = m.
And acceleration due to gravity = g.
Therefore, according to Newton’s Second Law of Motion which states that Force is the product
of mass and acceleration,
F = m x g -----------------(i)
Now, according to Universal Law of gravitation,
F G*M.m / d2 ……………. (ii)
Thus, from above two expressions, we get
Where, g is acceleration due to gravity,
G is the Universal Gravitational Constant.
M is the mass of earth.
And d is the distance between object and centre of earth.
WHEN OBJECT IS NEAR THE SURFACE OF EARTH
When an object is near the surface of earth, the distance between object and centre of the earth will be equal to the radius of earth because the distance of object is negligible in comparison of the radius of earth.
Let the radius of earth is equal to R.
Therefore, after substituting ‘R’ at the place of ‘d’ we get,
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