Force and Motion Dynamics

According to Newton's Shell Theorem, what is the gravitational force on an object located inside a uniform spherical shell?

A uniform sphere of mass $M$ and radius $R$ has a point mass $m$ located outside the sphere at a distance 2R from the center. What is the gravitational force on the point mass?

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

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

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?

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?

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

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?