A block is placed on an incline having inclination `theta` . There is a rigid L shaped frame fixed to the block. A plumb line (a ball connected to a thread) is attached to the end A of the frame. The system is released on the inline. Find the angle that the plumb line will make with vertical in its equilibrium position relative to the block when
(a) the incline is smooth
(b) there is friction and the acceleration of the block is half its value when the incline is smooth

Answer

(a) `theta`
(b) `tan^(-1) (("sin"theta. "cos"theta)/(2 - sin^(2) theta))`