Question

The gravitational force between two objects is F. If the distance between them is reduced to1/4 th. Now find the force between them.​

Answer 1

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Answer 2

Given,

The gravitational force between two objects = F

To find,

The gravitational force between the two objects when the distance between them is reduced to 1/4th.

Solution,

We can simply solve this numerical problem by using the following process:

Let us assume that the initial distance between two objects is R and the new distance between the two objects is R/4.

As per gravitational law;

The gravitational force acting between two bodies of mass M and m, separated by a distance d, is mathematically represented as;

F = (G ×M×m)/d^2,

where G = Gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2

Now, according to the question;

The force acting in the initial conditions-

F = (G ×M×m)/R^2

{Equation-1}

Now, according to the question, when the distance is reduced,

The force acting

= (G ×M×m)/(R/4)^2

= (G ×M×m)/R^2/16

= 16×(G ×M×m)/R^2

= 16×F

{according to equation-1}

Hence, the gravitational force between the two objects increases by 16 times when the distance between them is reduced to 1/4th.