4) A planet that has a hollow core consists of a uniform spherical shell with mass M, outer radius R, and innerradius R/2. Letr 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 ismoving 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 ismoving inside the planet.d. Given the potential energy of an object is described by the formula: U(x,y) = a(x² + y²) + bxy, where a andb are positive constants. Find the x component of the applied force.

Answered: 4) A planet that has a hollow core…

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