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title: "A uniform spherical star of mass \\(M\\) and initial radius \\(R_0\\) rotates with angular speed \\(\\omega_0\\). The star undergoes gravitational collapse, shrinking uniformly to a final radius \\(R_f = \\dfrac{R_0}{n}\\) (where \\(n > 1\\)) with no change in mass or spherical shape. Assuming no external torques act on the star, what is the ratio of the star’s final rotational kinetic energy to its initial rotational kinetic energy, \\(\\dfrac{K_f}{K_i}\\)?"
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url: "https://nerd-notes.com/ubq/120880/"
date_modified: "2026-08-23T04:44:06+00:00"
---

# A uniform spherical star of mass \(M\) and initial radius \(R_0\) rotates with angular speed \(\omega_0\). The star undergoes gravitational collapse, shrinking uniformly to a final radius \(R_f = \dfrac{R_0}{n}\) (where \(n > 1\)) with no change in mass or spherical shape. Assuming no external torques act on the star, what is the ratio of the star’s final rotational kinetic energy to its initial rotational kinetic energy, \(\dfrac{K_f}{K_i}\)?

A uniform spherical star of mass \(M\) and initial radius \(R_0\) rotates with angular speed \(\omega_0\). The star undergoes gravitational collapse, shrinking uniformly to a final radius \(R_f = \dfrac{R_0}{n}\) (where \(n > 1\)) with no change in mass or spherical shape. Assuming no external torques act on the star, what is the ratio of the star's final rotational kinetic energy to its initial rotational kinetic energy, \(\dfrac{K_f}{K_i}\)?

- **A.** \(n^2\)
- **B.** \(n\)
- **C.** \(\dfrac{1}{n^2}\)
- **D.** \(n^4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120880/*