A solid sphere rolls down two different inclined planes of...

Name: Problem 85, Chapter 7: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-28T14:39:07-08:00
Duration: 3 min 12 s
Channel: Dheeraj Sharma
Description: A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In both cases (a) the speed and time of descend will be same. (b) the speed will be same but time of descend will be different. (c) the speed will be different but time of descend will be same. (d) speed and time of descend both are different.

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In both cases (a) the speed and time of descend will be same. (b) the speed will be same but time of descend will be different. (c) the speed will be different but time of descend will be same. (d) speed and time of descend both are different.

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In both cases
(a) the speed and time of descend will be same.
(b) the speed will be same but time of descend will be different.
(c) the speed will be different but time of descend will be same.
(d) speed and time of descend both are different.

Key Concepts

Conservation of Energy

This concept explains how the potential energy that a solid sphere possesses due to its position at a certain height is converted into kinetic energy as it rolls down an inclined plane. For rolling objects, this kinetic energy is divided into translational kinetic energy (due to the center of mass moving) and rotational kinetic energy (due to the sphere spinning). Since the total mechanical energy is conserved (in the absence of non-conservative forces), the final speed at the bottom depends only on the height, not the specific path taken.

Rolling Without Slipping

Rolling without slipping is a condition where the sphere rotates in such a way that its point in contact with the surface is momentarily at rest relative to the surface. This condition establishes a relationship between the translational speed of the sphere’s center of mass and its angular speed. It ensures that the distribution of energy between translational and rotational forms is correctly accounted for in energy conservation calculations.

Dynamics on an Inclined Plane

The motion of a rolling sphere down an inclined plane is influenced by the angle of the incline. A steeper incline produces a larger component of gravitational acceleration along the plane, resulting in a higher acceleration and a shorter time of descent, even though the final speed (determined solely by the vertical height) remains constant for a given height.

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