Question

The gravitational force between two objects is 49 N. How much distance between these objects be decreased so that the force between them becomes double?​

Answer 1

Answer:

The gravitational force of attraction between the bodies is inversely proportional to the square of the distance of seperation between them .

F proportional to 1/r^2

if the mass of the two bodies are same.

We can write

F1 proportional to 1/r1^2

F2 proportional to 1/r2^2

In the form of proportion

F1/F2 = r2^2/r1^2

F1 = 49N × 2 = 98N

F2= 49N

98/49 = r2^2/r1^2

2/1 = (R2/R1)^2

R2/R1 = √2

R1/R2 = 1/√2

The distance of seperation should be decreased by 1/√2 of the previous one so the force between the two bodies becomes doubled.