Question

In the figure, the minimum value of a at which the cylinder starts rising up the inclined surface is:

• A. $gtan\theta$
• B. $gcot\theta$
• C. $gsin\theta$
• D. $gcos\theta$

Answer 1

The correct option is A $gtan\theta$

The cylinder experiences a pseudo acceleration $a$ in left direction and $g\sin \theta$ along the incline.
For it to rise up, the acceleration along incline should just be greater than zero. In the limiting case,
pseudo acceleration along incline is $a\cos \theta$
Thus, $a\cos \theta =g\sin \theta$
$a=g\tan \theta$