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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

A solid sphere, a hollow sphere, and a disc, all sharing identical...

A solid sphere, a hollow sphere, and a disc, all sharing identical mass and radius, are positioned at the top of an incline and released. The friction coefficients between the objects and the incline are identical and are insufficient to permit pure rolling. The minimum time to reach the bottom will be taken by

Options

  1. Aall will require the same time
  2. Bthe solid sphere
  3. Cthe hollow sphere
  4. Dthe disc

Correct answer

A. all will require the same time

Step-by-step solution

Since the friction is insufficient to permit pure rolling, all the objects will slip as they move down the incline.

The kinetic friction acting on each object is fk=μmgcos⁡θf_k = \mu mg \cos \theta.

The equation of motion for the center of mass is given by mgsin⁡θ−fk=mamg \sin \theta - f_k = ma.

Substituting the value of fkf_k, we get a=g(sin⁡θ−μcos⁡θ)a = g(\sin \theta - \mu \cos \theta).

The linear acceleration aa is independent of the shape, mass, radius, and moment of inertia of the objects.

Since all objects are released from rest and travel the same distance along the incline with the same acceleration, they will all require the same time to reach the bottom.
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