In the system shown in fig., block A and C are placed on smooth floors and both have mass equal to `m_(1)`. Blocks B and D are identical having mass `m_(2)` each. Coefficient of friction

Between A and B and that between C and D are both equal to `mu`. String and pulleys are light. A horizontal force F is applied on block C and is gradually increased.
(a) Find the maximum value of F (call it `F_(0)`) so that all the four blocks move with same acceleration.
(b) Will the value of `F_(0)` increase or decrease if another block (E) of mass `m_(2)` is placed above block D and coefficient of friction between E and D is `mu`?

Answer

`F_(0) = 2 mum_(2) g ((m_(2) + m_(1))/(2m_(2) + m_(1)))` ; increase