---
title: "A uniform solid sphere and a thin hollow spherical shell, each having mass \\(M\\) and radius \\(R\\), are suspended from frictionless horizontal pivots attached to their topmost points, as shown. When both spheres are displaced by the same small initial angle and released from rest, the hollow shell is observed to oscillate with a longer period than the solid sphere. Which of the following best explains why the hollow spherical shell has a longer oscillation period than the solid sphere?"
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url: "https://nerd-notes.com/ubq/124517/"
date_modified: "2026-09-28T14:08:27+00:00"
---

# A uniform solid sphere and a thin hollow spherical shell, each having mass \(M\) and radius \(R\), are suspended from frictionless horizontal pivots attached to their topmost points, as shown. When both spheres are displaced by the same small initial angle and released from rest, the hollow shell is observed to oscillate with a longer period than the solid sphere. Which of the following best explains why the hollow spherical shell has a longer oscillation period than the solid sphere?

A uniform solid sphere and a thin hollow spherical shell, each having mass \(M\) and radius \(R\), are suspended from frictionless horizontal pivots attached to their topmost points, as shown. When both spheres are displaced by the same small initial angle and released from rest, the hollow shell is observed to oscillate with a longer period than the solid sphere. Which of the following best explains why the hollow spherical shell has a longer oscillation period than the solid sphere?

![Two separate line drawings side by side against a white background, each depicting a sphere suspended from a horizontal ceiling. On the left, labeled Solid sphere, a shaded gray circle represents a solid sphere of radius \(R\) and mass \(M\). A small black circular pivot dot is fixed to the top edge of the circle and connected to the ceiling line. A vertical dashed line passes through the pivot dot and the center of the circle. On the right, labeled Spherical shell, an unshaded white circle with a thick dark circular outline represents a thin spherical shell of the same radius \(R\) and mass \(M\), attached to a ceiling line by a small black circular pivot dot at its top edge, with an identical vertical dashed centerline. Both circles show a horizontal dashed line segment indicating the radius labeled \(R\) from the center to the right edge. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604507-OKAcHc.jpg)

- **A.** The hollow shell experiences a smaller gravitational restoring torque at any displacement angle because its mass is concentrated along the outer shell rather than distributed near the center of mass, resulting in a lower angular acceleration throughout the oscillation.
- **B.** Both spheres experience the same gravitational restoring torque at any displacement angle because their centers of mass are equidistant from the pivot, but the shell's mass is located farther from its center of mass, giving it a larger rotational inertia about the pivot and a smaller angular acceleration.
- **C.** The solid sphere has a larger rotational inertia about the pivot because mass distributed throughout its volume provides greater rotational resistance, requiring the restoring torque to do more work and allowing the pendulum to swing through its arc in a shorter time.
- **D.** Both spheres have identical rotational inertia about the pivot because their total mass and pivot-to-center-of-mass distance are equal, but the shell's hollow interior stores less mechanical energy during the swing, causing it to move at a lower angular speed throughout the cycle.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124517/*