Answered: A hoop and a disck are released from…

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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Question

A hoop and a disck are released from the top of an incline at the same time. Which one will reach the bottom first?

A) whichever is heavier

B) hoop

C) both arrive at the same time

D) disk

Expert Solution

Step 1

Apply principle of conservation of energy

$E_{P} = E_{T} + E_{R} m g h = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$

For hoop all the masses are concentrated at the rim and for the disc it is uniformly distributed throughout. So, the moment of inertia for hoop is larger than the momentum of inertia of the disc.

Moment of inertia of hoop and disc

$I_{hoop} = m r^{2} I_{disc} = \frac{1}{4} m r^{2}$

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