A solid sphere, a disc and a ring of the same mass and radius are allowed to roll down a frictionless inclined plane simultaneously from the same height. In this context, which one of the following statements is correct?

examrobotsa's picture

Submitted by examrobotsa on

Q: 84 (CDS-I/2002)
A solid sphere, a disc and a ring of the same mass and radius are allowed to roll down a frictionless inclined plane simultaneously from the same height. In this context, which one of the following statements is correct?

question_subject: 

Science

question_exam: 

CDS-I

stats: 

0,16,24,10,11,3,16

keywords: 

{'solid sphere': [0, 0, 1, 0], 'sphere': [2, 0, 8, 5], 'disc': [1, 0, 1, 4], 'radius': [0, 0, 2, 2], 'plane': [0, 0, 4, 8], 'ring': [4, 0, 2, 6], 'same height': [0, 0, 2, 1]}

The correct answer is option 4 - All of them reach down simultaneously. This means that the solid sphere, the disc, and the ring will all reach the bottom of the inclined plane at the same time.

The reason for this is that they all have the same mass and radius. When objects of the same mass and radius roll down a frictionless inclined plane, their time of descent is independent of their shape.

This can be explained by considering their moments of inertia. The solid sphere, the disc, and the ring all have different moments of inertia, which determine how their mass is distributed in relation to the axis of rotation. However, in this scenario, the objects are rolling without slipping, which means that all of their moments of inertia are equal. Therefore, they experience the same force and acceleration down the incline.

Since the objects experience the same force and acceleration, they will all reach the bottom of the incline at the same time, regardless of their shape or mass distribution. So, option 4 is the correct statement.