The force of gravitation between two bodies varies with r as:a)...
Force of gravitation is inversely proportional to square of distance 1/r^2
The force of gravitation between two bodies varies with r as:a)...
The force of gravitation between two bodies is given by Newton's Law of Gravitation, which states that the force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = G * (m1 * m2) / r^2
where F is the force of gravitation, G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between them.
Now let's analyze the given options:
a) r^2: If the force varied with r^2, then it would mean that the force of gravitation decreases with the square of the distance. This is not consistent with Newton's Law of Gravitation, which states that the force decreases with the inverse square of the distance.
c) r: If the force varied with r, then it would mean that the force of gravitation decreases linearly with the distance. Again, this is not consistent with Newton's Law of Gravitation.
d) 1/r: If the force varied with 1/r, then it would mean that the force of gravitation increases as the distance between the bodies decreases. This is also not consistent with Newton's Law of Gravitation.
Therefore, the correct option is b) 1/r^2, which means that the force of gravitation decreases with the square of the distance between the bodies. This is in accordance with Newton's Law of Gravitation and is the correct expression for the force of gravitation.