### Determining Free-Fall Acceleration on a New Planet Using a Pendulum**Problem Statement:**You land on a new planet and would like to figure out its freefall acceleration, \( g_p \). You make a pendulum out of a solid disk as shown below:![Diagram of solid disk pendulum](cosmetic-description)In the diagram:- The solid disk is colored yellow.- The pendulum is pivoted at a point just outside its circumference.- The disk is depicted with its radius \( R \) extending from the center to the edge.- The center of mass (COM) of the disk is indicated by a blue "x," located a distance of \( R/2 \) from the circumference.- A dotted line represents the path the COM will follow as the disk oscillates.- \( \theta_0 \) is the small initial angle of displacement from the vertical.**Given Data:**- Total mass of disk, \( m = 2 \) kg- Radius of disk, \( R = 0.25 \) m- Period of oscillation, \( T = 1.5 \) s**Objective:**To determine the acceleration due to gravity, \( g_p \), on the new planet.**Explanation of the Diagram:**The diagram is a side view of a pendulum made from a solid disk. The pendulum is fixed at a point on the edge of the disk and allowed to oscillate. The initial displacement angle \( \theta_0 \) is very small. The center of mass (COM) of the disk is marked with a blue "x," which is at a distance \( R/2 \) from the pivot point. This distance forms the effective length of the pendulum.**Steps to Determine \( g_p \):**1. **Identify the effective length of the pendulum, \( L \)**: This is the distance from the pivot point to the center of mass of the disk. For a solid disk, this distance is \( R/2 \).2. **Use the formula for the period of a physical pendulum**: \[ T = 2\pi \sqrt{\frac{I}{mgL}} \] Where: - \( I \) is the moment of inertia of the disk about the pivot. - \( m \) is the mass of the disk. - \( g

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Description: ### Determining Free-Fall Acceleration on a New Planet Using a Pendulum**Problem Statement:**You land on a new planet and would like to figure out its freefall acceleration, \( g_p \). You make a pendulum out of a solid disk as shown below:![Diagram

Time period for the compound pendulum is given by the formula T=2πIcm+mL2mgLWhere Icm is the moment…

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6. You land on a new planet and would like to figure out its freefall acceler- ation, gp. You make a pendulum out of a solid disk as seen below: Joo R/2 Suppose the disk has total mass m = 2 kg and radius R = 0.25 m. Its COM is indicated by the blue "x" on the diagram, a distance of R/2 from the circumference. Ensuring that is very small, you let the pendulum oscillate and measure that its total period is T = 1.5 s. What is gp?

6. You land on a new planet and would like to figure out its freefall acceler- ation, gp. You make a pendulum out of a solid disk as seen below: Joo R/2 Suppose the disk has total mass m = 2 kg and radius R = 0.25 m. Its COM is indicated by the blue "x" on the diagram, a distance of R/2 from the circumference. Ensuring that is very small, you let the pendulum oscillate and measure that its total period is T = 1.5 s. What is gp?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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