Force of Gravity and Gravitational Potential Energy Functions from Zero to Infinity (but not beyond)

The video tutorial explores Newton's universal law of gravitation, focusing on the equations for gravitational force and potential energy. It discusses graphing these forces both outside and inside a planet, assuming constant density and non-rotation. The tutorial explains the derivation of equations, including Newton's shell theorem, and analyzes the graphs of gravitational force and potential energy, highlighting their relationships and differences.

What is the relationship between the force of gravity and the distance r when the object is outside the planet?

• Proportional to r squared

• Proportional to the inverse of r squared

• Proportional to r

• Proportional to the inverse of r

What assumption is made about the planet's density when considering an object inside it?

• The density increases with depth

• The density is constant

• The density decreases with depth

• The density varies randomly

According to Newton's shell theorem, what happens to the gravitational forces from the mass outside the radius r?

• They have no effect

• They cancel out

• They decrease the net force

• They add up to increase the net force

How is the mass inside a hypothetical sphere calculated in terms of density?

• Density minus the volume of the sphere

• Density divided by the volume of the sphere

• Density times the volume of the sphere

• Density plus the volume of the sphere

What is the nature of the force of gravity acting on an object inside the planet?

• Exponential

• Quadratic

• Linear

• Constant

What mathematical operation is used to derive the gravitational potential energy inside the planet?

• Differentiation

• Division

• Integration

• Multiplication

What is the shape of the gravitational potential energy function inside the planet?

• Parabolic

• Exponential

• Linear

• Constant

At what point do the two gravitational potential energy equations have the same value?

• At the core of the planet

• At the edge of the universe

• At the surface of the planet

• At the center of the planet

What is the initial slope of the gravitational potential energy graph at r equals 0?

• Undefined

• Zero

• Negative

• Positive

How does the magnitude of the force of gravity change as r increases from the radius of the Earth?

• It remains constant

• It oscillates

• It increases

• It decreases