Question

Figure given shows a smooth inclined plane fixed in a car accelerating on horizontal road. The angle of incline $\theta$ is related to the acceleration a of the car as $a=g\tan \theta$. If the sphere is set in pure rolling on the incline.

• A. it will continue pure rolling.
• B. it will slip down the plane.
• C. its linear velocity will increase.
• D. its linear velocity will decrease.

Answer 1

The correct option is A it will continue pure rolling.

Option (A) is correct.

Given that $a=g\tan \theta$
According to free body diagram

Net force on sphere along incline

$F_{net}=mg\sin \theta -ma\cos \theta$

Put the value of a i,e. $g\tan \theta$

$F_{net}=mg\sin \theta -mg\tan \theta .\cos \theta$

$F_{net}=mg\sin \theta -mg\sin \theta$

$F_{net}=0$

So, if the sphere is set in pure rolling on the incline, it will continue pure rolling.