Question

state universal law of gravitation. the gravitational force between two objects is 100 N. how should the distance between the object be changed so that the force between them becomes 50 N

Answer 1

a law stating that any two masses attract each other with a force equal to a constant (constant of gravitation) multiplied by the product of the two masses and divided by the square of the distance between them. Expand. Also called law of universal gravitation. Origin of law of gravitation
F1 = G M m / d1²
F2 = G M m / d2²

F1 / F2 = d2² / d1²

100 / 50 = (d2/d1)²

d2 = √2 d1

distance should be  √2 times the previous.

Answer 2

Hey! 

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Universal law of gravitation states -

• Every object in the universe attracts every other object with a force which is directly proportional to the product of their masses.

• Every object in the universe attracts every other object with a force which is inversely proportional to the square of the distance between their centers. The direction of the force is alone the line joining the center's of two objects.

DERIVATION OF UNIVERSAL LAW OF GRAVITATION-

Suppose there are two object, A and B with masses, m1 and m2 respectively and 'r' is the distance between them.

According to the first point of Newton's law of gravitation-

F∝m1 × m2 [i]

According to second point of Newton's law of gravitation-

F∝ 1/r^2 [ii]

Combining [i] and [ii],

F ∝ m1×m2/r^2

So,

F= Gm1m2/r^2

Where, G= Universal gravitational constant.


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Numerical -

F1= 100 N
F2= 50 N

Let original distance be r1 and new distance between the two objects be r2

We know, F∝1/r^2

F1/^F2= (r1/r2)^2
100/50= 2

r1/r2 = √2, r^2 = √2 r1

Distance between the object should be increased by √2 times


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Hope it helps...!!!