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

Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter4: Forces In One Dimension
Section4.2: Weight And Drag Force
Problem 24SSC
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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

EP=ET+ERmgh=12mv2+12Iω2

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

Ihoop=mr2Idisc=14mr2

 

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