The figure shows a smooth inclined plane of inclination θ fixed in a car. A sphere is set in pure rolling on…

The figure shows a smooth inclined plane of inclination $\mathrm{\theta }$ 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?

1. $g\cos \theta$
2. $g\sin \theta$
3. $g\cot \theta$
4. $g\tan \theta$

Solution

The sphere will continue pure rolling if

$\mathrm{ma}\mathrm{ }\cos \mathrm{\theta }=\mathrm{ }\mathrm{m}\mathrm{g}\mathrm{ }\sin \mathrm{\theta }$

or $\mathrm{a}=\mathrm{g}\mathrm{ }\tan \mathrm{\theta }$

Asked in: JEE Mains - Rotational Motion - Chapter Test

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