A solid sphere, disc, and solid cylinder all of the same...

Name: Problem 92, Chapter 5: Objective Physics : NEET 2020 Examination textbook Gurukul Oswal
Uploaded: 2021-10-01T16:12:05-08:00
Duration: 1 min 57 s
Channel: Dheeraj Sharma
Description: A solid sphere, disc, and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on an inclined plane, then (a) solid sphere reaches the bottom first. (b) solid sphere reaches the bottom last. (c) disc will reach the bottom first. (d) all reach the bottom at the same time.

A solid sphere, disc, and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on an inclined plane, then (a) solid sphere reaches the bottom first. (b) solid sphere reaches the bottom last. (c) disc will reach the bottom first. (d) all reach the bottom at the same time.

A solid sphere, disc, and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on an inclined plane, then
(a) solid sphere reaches the bottom first.
(b) solid sphere reaches the bottom last.
(c) disc will reach the bottom first.
(d) all reach the bottom at the same time.

Key Concepts

Rolling Without Slipping

Rolling without slipping is a condition where the point of contact between the rolling object and the surface has zero relative velocity. This condition establishes a connection between an object's translational and rotational motion, ensuring that the link v = ?r holds. It is essential in analyzing the dynamics of rolling objects on an inclined plane.

Rolling Motion

Rolling motion involves a combination of translational and rotational movement where an object rotates about its own axis while its center of mass moves along a path. In the absence of slipping, the angular velocity is directly related to the translational velocity, making the dynamics of rolling dependent on both forms of motion.

Moment of Inertia

The moment of inertia is a measure of how an object's mass is distributed relative to an axis of rotation. It plays a crucial role in rotational dynamics because it determines the resistance an object has to changes in its rotational state. In problems involving rolling, objects with lower moments of inertia relative to their mass tend to accelerate faster down an incline.

Energy Conservation

In rolling motion, gravitational potential energy is converted into both translational kinetic energy and rotational kinetic energy. The specific distribution between these two forms depends on the object's moment of inertia. By applying energy conservation principles, one can derive the relationship between the incline’s height and the speeds of different objects as they roll down.

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