Question

UNIVERSAL LAW OF GRAVITATION
Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects.
Let two objects A and B of masses M and m lie at a distance d from each other as shown in the fig. . Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses.
That is,
F M × m -------------- (1)
And the force between two objects is inversely proportional to the square of the distance between them, that is,
F 1 -------------- (2) 2
Combining Equations. (1) and (2), we get,
F × ---------------- (3) 2
F = G x × ----------------- (4) 2
Where,
G is the constant of proportionality and is called the universal gravitation constant, 6.67 x 10-11 Nm2kg-2.
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VALUE OF ACCELERATION DUE TO GRAVITY ON THE SURFACE OF THE EARTH,g
According to Newton's universal law of gravitation, F = ---------------------(1)
2
where,
F is force experienced by object of mass, m due to earth gravitational force of the earth on the object.
G is the constant of proportionality and is called the universal gravitation constant, 6.67 x 10-11 Nm2kg-2.
M is the mass of the earth, 6 x 1024 kg. m is the mass of the object.

d is the radius of the earth, 6400 km.
According to Newton’s second law,
F = ma;
Here a = acceleration due to gravity, g. Hence, F = mg ---------------- (2)
Equating (1) and (2), we get, mg =
2
Cancelling ‘m’ on both sides, g =
2
g = 6.67 10−11 6 1024 (6.4 106)2
g = 9.8 ms-2.
Hence, value of g = 9.8 m/s2

Answer 1

Answer:

G=6.67*10-¹¹

THIS IS ALWAYS CONSTANT