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Nine small particles, each with mass m, are evenly arranged around a ring of radius R. (a) Calculate the net gravitational force on one of the particles due to the other eight particles in the ring. (b) Find the rotational period of the ring necessary to prevent the ring from collapsing under the mutual gravitational attraction of the particles.

Nine small particles, each with mass m, are evenly arranged around a ring of radius R. (a) Calculate the net gravitational force on one of the particles due to the other eight particles in the ring. (b) Find the rotational period of the ring necessary to prevent the ring from collapsing under the mutual gravitational attraction of the particles.

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
9 years ago
(a)
The figure which shows the arrangement of the nine particles is shown below:
235-276_im12.JPG
Apply cosine law to the triangle OAB, the distance r is given by

235-1503_im13.JPG
The net force due to the system of particles is
235-1741_im14.JPG
235-672_im15.JPG
235-1959_im16.JPG

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