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

Answer:

the distance should be changed by a factor of √2

Explanation:

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

$F =\frac{Gm_1m_2}{r^2}$

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:

$F' = \frac{1}{2} F = \frac{1}{2} \frac{Gm_1m_2}{r^2}\\\\F' = \frac{1}{2} F = \frac{Gm_1m_2}{(\sqrt{2}r)^2}$

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