Question

A couple is sitting side-by-side. By what factor should the distance between them be changed by if the attractive force is to be halved?

Answer 1

the distance should be changed by a factor of √2

Step-by-step explanation:

The attractive force between the couples can be given by Newton's Law of Gravitation:

`F =(Gm_1m_2)/(r^2)`

where,

F = Attractive Force

G = Universal Gravitational Constant

m₁ = mass of the first person

m₂ = mass of the second person

r = distance between them

Now, if we want to halve the force without changing masses, hen:

`F' = (1)/(2) F = (1)/(2) (Gm_1m_2)/(r^2)\\\\F' = (1)/(2) F = (Gm_1m_2)/((√(2)r)^2)`

Hence, it is clear that the distance should be changed by a factor of √2