Two objects, with masses m1 and m2, are originally a distance r apart. The gravitational force between them has magnitude F. The second object has its mass changed to 2m2, and the distance is changed to r/4. What is the magnitude of the new gravitational force?

(A) 16F
(B) 32F
(C) F/16
(D) F/32

The gravitational force will increase 32 times , if mass of m2 is increase 2 times and distance between them is decreased by 4 times.

Newton's law of universal gravitation,

Where,

F =force

G =gravitational constant

m1=mass of object 1

m2 =mass of object 2 =  2 x m2

r =distance between centers of the masses = r/4

So, new gravitational force,

Therefore, the gravitational force will increase 32 times , if mass of m2 is increase 2 times and distance between them is decreased by 4 times.

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The magnitude of the new gravitational force becomes 32 times of the original force.

Explanation:

Two objects, with masses m₁ and m₂, are originally a distance r apart. the gravitational force between them is given by :

If the second object has its mass changed to 2m₂ and the distance is changed to r/4, such that,

and

The new gravitational force is given by :

So, the magnitude of the new gravitational force becomes 32 times of the original force. Hence, the correct option is (B) "32F".

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