The arrangement shown in figure is in equilibrium with all strings vertical. The end A of the string is tied to a ring which can be slid slowly on the horizontal rod. Pulley `P_(1)` is rigidly fixed but `P_(2)` can move freely. A mass m is attached to the centre of pulley `P_(2)` through a thread. Pulleys and strings are mass less.

(a) Which block will move up as A is moved slowly to the right?
(b) Will the block of mass m have horizontal displacement?
(c) Is it possible, for a particular position of A, that M has no acceleration but m does have an acceleration? If this happens when string from `P_(2)` to A makes an angle `theta` with vertical, find the acceleration of m at the instant.

Answer

(a) Block with mass M will move up.
(b) yes
(c) `g (1 - "cos"theta)`