4) A planet that has a hollow core consists of a uniform spherical shell with mass M, outer radius R, and inner radius R/2. Let r be the distance from the center of the planet. a. Derive an expression for the gravitational force on a small mass as a function of r when it is moving outside the planet. b. Find the period T of a satellite if it orbits very near the surface of the planet. c. Derive an expression for the gravitational force on a small mass as a function of r when it is moving inside the planet. d. Given the potential energy of an object is described by the formula: U(x,y) = a(x² + y?) + bxy, where a and

Q: need help with part b i solved a prior

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Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.