Two concentric spherical shells with uniformly distributed masses M1 = 471 kg an

Question

Two concentric spherical shells with uniformly distributed masses M1 = 471 kg and M2 = 767 kg are situated as shown in the figure. Find the magnitude of the net gravitational force on a particle of mass m = 22 kg, due to the shells, when the particle is located at radial distance (a) a = 36 m, (b) b = 18 m, and (c) c = 2.1 m. Please provide numeric answers, not just answers with variables. That is in the book, I am not understanding how to apply those variables. So please provide numeric answer.

Explanation / Answer

For a shell if a mass is outside it, for purposes of calculating gravitational force we can assume it to be a point mass at the center

Hence for distace = 36 m
We have gravitational force = GM1m/a2 + GM2m/a2 = (6.67300*10-11*(471+767)*22)/362 = 1.402*10-9 N

For a shell we have 0 gravitational force due to it inside it.
Hence when we have particle at distance b; the outer shell exerts no force
Hence We have gravitational force = GM1m/b2 = (6.67300*10-11*471*22)/182 = 2.134*10-9 N

Finally when particle is at c it is inside both shells and thus we have Gravitational force = 0 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.