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A small, light pulley is attached with a...

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.

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The correct Answer is:
5
Let vertically downward component of acceleration of A be a and let acceleration of C be c (rightward). Then horizontal component of acceleration of A is c (rightward) and acceleration of B, relative to C is a leftward. Hence resultant acceleration of B is `(a-c)` leftward. Now considering free body diagram

For block A, `H=2c` ....(i)
`2g-T=2a` ....(ii)
For horizontal force on block B,
`T=1.5(a-c)` ....(iii)
From above equations, `a=6.25 ms^(-2) and c=1.25 ms^(-2)`
:. Vertical acceleration of `A=a=6.25 ms^(-2)` (downward)
Horizontal acceleration of `A=c=1.25 ms^(-2)` (rightward)
Acceleration of `B=(a-c)=5ms^(-2)` (leftward)
Acceleration of `C=c=1.25ms^(-2)` (rightward)
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