In the fig. shown, the pulley and string are mass less and the incline is frictionless. The segment AP of the string is parallel to the incline and the segment PB is perpendicular to the incline. End of the string is pulled with a constant force F.
(a) If the block is moving up the incline with acceleration while being in contact with the incline , then angle `theta` must be less than `theta_(0)`. Find `theta_(0)`
If `theta = (theta_(0))/(2)` find the maximum acceleration with which the block can move up the plane without losing contact with the incline.

Answer

(a) `theta_(0) = (pi)/(4)`
(b) `a_("max") = g[cos((pi)/(8)) - sin((pi)/(8))]`