A small, light pulley is attached with a block C of mass 4 kg as shown in fig A block B of mass `1.5kg` is placed on the top horizontal surface of C. Another block A of mass 2 kg is hanging from a string, attached with B and passing over the pulley. Taking `g=10 ms^(-2)` and neglecting friction, acceleration of block C when the system is released from rest is `x//4` calculate x.

Answer

5

Explanation

Let vertically downward component of acceleration of A be a and let acceleration of `C` be c (right ward) Then horizontal component of acceleration of `A` is (right ward) and acceleration of `B` relative to `C` is a leftward Hence resultant acceleration of `B` is (a c) left ward. Now considering free body diagram
For block `A, H= 2c....(1) 2g -T =2a...(2)`
For horizontal forces on block `B`
`T =1.5 (a-c)...(3)` from above equations,
`:.` Vertical acceleration of `A=a=6.25ms^(-2)` (downward)
Horizontal acceleration of A `= c = 1.25 ms^(-2)` (right ward)
Acceleration of `B = (a-c) =5ms^(-2)` (left ward)
Accleration of `C = C =1.25 ms^(-2)` (right ward)
.