In the arrangement shown in figure pulley P can move whereas other two pulleys are fixed. All of them are light. String is light and inextensible. The coefficient of friction between 2 kg and 3 kg block is `mu = 0.75` and that between 3 kg block and the table is `mu = 0.5`. The system is released from rest

(i) Find maximum value of mass M, so that the system does not move. Find friction force between 2 kg and 3 kg blocks in this case.
(ii) If M = 4 kg, find the tension in the string attached to 2 kg block.
(iii) If M = 4 kg and `mu_(1) = 0.9`, find friction force between the two blocks, and acceleration of M.
(iv) Find acceleration of M if `m_(1) = 0.75, m_(2) = -0.9` and M = 4 kg.

Answer

(i) 2.5 kg ; 12.5 N (ii) `(50)/(3) N `
(iii) `(40)/(3) N , a = (5)/(3) m//s^(2)`
(iv) `(5)/(6) m//s^(2)`