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title: "A thick spherical shell of uniform mass density has an inner radius \\(R_1\\), an outer radius \\(R_2\\), and a total mass \\(M\\). A point particle of mass \\(m\\) is located at a distance \\(r\\) from the center of the shell, where \\(R_1 < r < R_2\\). In terms of the given quantities and the universal gravitational constant \\(G\\), which of the following expressions represents the magnitude of the net gravitational force exerted by the shell on the particle?"
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url: "https://nerd-notes.com/ubq/120557/"
date_modified: "2026-08-23T04:41:35+00:00"
---

# A thick spherical shell of uniform mass density has an inner radius \(R_1\), an outer radius \(R_2\), and a total mass \(M\). A point particle of mass \(m\) is located at a distance \(r\) from the center of the shell, where \(R_1 < r < R_2\). In terms of the given quantities and the universal gravitational constant \(G\), which of the following expressions represents the magnitude of the net gravitational force exerted by the shell on the particle?

A thick spherical shell of uniform mass density has an inner radius \(R_1\), an outer radius \(R_2\), and a total mass \(M\). A point particle of mass \(m\) is located at a distance \(r\) from the center of the shell, where \(R_1 < r < R_2\). In terms of the given quantities and the universal gravitational constant \(G\), which of the following expressions represents the magnitude of the net gravitational force exerted by the shell on the particle?

![A cross-sectional diagram showing two concentric circles centered at a common origin labeled O. The inner circle has a radius labeled R_1 with a dashed arrow from the center to its boundary. The outer circle has a radius labeled R_2 with a dashed arrow from the center to its boundary. The region between the inner and outer circles is shaded with light gray diagonal hatching. A small solid black dot representing a point mass is located in the shaded region between the two circular boundaries at a distance r from the center, with a solid line extending from O to the dot labeled r and the dot labeled m. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460095-WBfVWp.jpg)

- **A.** \(\dfrac{G M m r}{R_2^3}\)
- **B.** \(\dfrac{G M m (r^2 - R_1^2)}{r^2 (R_2^2 - R_1^2)}\)
- **C.** \(\dfrac{G M m (r^3 - R_1^3)}{r^2 (R_2^3 - R_1^3)}\)
- **D.** \(\dfrac{G M m (R_2^3 - r^3)}{r^2 (R_2^3 - R_1^3)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120557/*