Force and Motion Dynamics

According to Newton's Law of Universal Gravitation, how does the gravitational force between two objects change if the distance between their centers of mass is doubled?

Two objects with masses $m_1 = 10 ext{ kg}$ and $m_2 = 20 ext{ kg}$ are separated by a distance of $r = 2 ext{ m}$. What is the gravitational force between them? (Use $G = 6.67 imes 10^{-11} ext{ N m}^2/ ext{kg}^2$)

Three identical masses ($m$) are placed at the vertices of an equilateral triangle with side length $a$. What is the magnitude of the gravitational force on one mass due to the other two?

What is the definition of gravitational field strength ($g$) at a point in space?

A $50 ext{ kg}$ object experiences a gravitational force of $490 ext{ N}$ at a certain location. What is the gravitational field strength at that location?

A charged particle moves in a non-uniform gravitational field. Which of the following factors will affect its motion?

An object has a mass of $10 ext{ kg}$ on Earth, where the gravitational acceleration is approximately $10 ext{ m/s}^2$. What is its weight?

An object weighs $200 ext{ N}$ on Earth, where the gravitational acceleration is $9.8 ext{ m/s}^2$. On Planet X, the gravitational acceleration is $4.9 ext{ m/s}^2$. What is the weight of the object on Planet X?

A person is standing in an elevator. Under what condition will their apparent weight be less than their actual weight?

A $60 ext{ kg}$ person is in an elevator accelerating upwards at $2 ext{ m/s}^2$. What is their apparent weight? (Use $g = 10 ext{ m/s}^2$)