---
title: "A simple pendulum consisting of a small sphere of mass \\(M\\) attached to the end of a light string of length \\(L\\) oscillates with a small amplitude and period \\(T\\). If the sphere is replaced by one of mass \\(2M\\) while the length \\(L\\) and the initial angular amplitude remain unchanged, which of the following statements correctly compares the new period to \\(T\\) and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/120958/"
date_modified: "2026-08-23T04:44:43+00:00"
---

# A simple pendulum consisting of a small sphere of mass \(M\) attached to the end of a light string of length \(L\) oscillates with a small amplitude and period \(T\). If the sphere is replaced by one of mass \(2M\) while the length \(L\) and the initial angular amplitude remain unchanged, which of the following statements correctly compares the new period to \(T\) and provides the correct physical justification?

A simple pendulum consisting of a small sphere of mass \(M\) attached to the end of a light string of length \(L\) oscillates with a small amplitude and period \(T\). If the sphere is replaced by one of mass \(2M\) while the length \(L\) and the initial angular amplitude remain unchanged, which of the following statements correctly compares the new period to \(T\) and provides the correct physical justification?

- **A.** The new period is greater than \(T\) because the increased inertia of the larger mass reduces the angular acceleration for any given displacement.
- **B.** The new period is less than \(T\) because the doubled mass doubles the gravitational restoring torque, increasing the angular acceleration at all displacements.
- **C.** The new period is equal to \(T\) because the gravitational restoring torque acting on the sphere is independent of its mass.
- **D.** The new period is equal to \(T\) because the doubling of the gravitational restoring torque is exactly offset by the doubling of the sphere's rotational inertia.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120958/*