Question

The figure shows a smooth inclined plane of inclination $\theta $ fixed in a car. A sphere is set in pure rolling on the incline. For what value of the acceleration of the car in the horizontal direction the sphere will continue pure rolling?

• A. $g \, \cos \theta $
• B. $g \,\sin \theta $
• C. $g \, \cot \theta $
• D. $g \, \tan \theta $

Answer 1

Answer: (D)

The sphere will continue pure rolling if
$ma \, \cos \theta = \, mg \, \sin ⁡ \theta $
or $ \, a=g \, \tan \theta $