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

Name: Problem 104, Chapter 7: Objective Physics for NEET
Uploaded: 2021-09-11T02:35:33-08:00
Duration: 3 min 28 s
Channel: Dheeraj Sharma
Description: A solid sphere rolls down two different inclined planes of the same height but of different inclinations (a) in both cases, the speeds and time of descent will be same. (b) the speeds will be same but time of descent will be different. (c) the speeds will be different but time of descent will be same. (d) speeds and time of descent both will be different.

A solid sphere rolls down two different inclined planes of the same height but of different inclinations (a) in both cases, the speeds and time of descent will be same. (b) the speeds will be same but time of descent will be different. (c) the speeds will be different but time of descent will be same. (d) speeds and time of descent both will be different.

A solid sphere rolls down two different inclined planes of the same height but of different inclinations
(a) in both cases, the speeds and time of descent will be same.
(b) the speeds will be same but time of descent will be different.
(c) the speeds will be different but time of descent will be same.
(d) speeds and time of descent both will be different.

Key Concepts

Conservation of Energy

In rolling motion, the gravitational potential energy of a body at a given height is converted into both translational and rotational kinetic energy as it descends. This energy conversion is independent of the path taken, meaning that objects starting from the same height will have the same speed at the bottom regardless of the incline’s steepness, provided there are no losses due to frictional slipping or air resistance.

Rolling Motion

Rolling motion involves both translational and rotational movement, linked by the no-slip condition which relates the linear velocity to the angular velocity. The moment of inertia plays a crucial role in determining how much energy is partitioned into rotation versus translation. Thus, while the final speeds may be equal for objects starting from the same height, the path’s inclination affects the acceleration and, consequently, the time needed for the descent.

Dynamics of Inclined Planes

The dynamics of inclined planes show that while the potential energy change is the same for a given height, the acceleration along the incline depends on the angle of the plane. A steeper incline provides a larger component of gravitational force, leading to a higher acceleration and a shorter descent time, even though the total energy conversion and final speed remain consistent with that of a less steep but longer inclined path.

Transcript

Please give Ace some feedback