Question

In the system shown, block $A$ is of mass $4.0\, kg$ and blocks $B$ and $C$ are of equal mass each of $3\, kg$. Find the acceleration in $m / s ^{2}$ of block $C$, if the system is set free. $\left[g=10\, m / s ^{2}\right.$ ]

Answer 1

$F.B.D$. of the blocks $A, B$ and $C$

Conditions of forces on $B$ and $C$ are same so they both will move with same downward acceleration $a$.
The block $A$ moves with the same acceleration $a$ upwards
From block $A: 2 T-40=4 a$ ...(i)
From block $B$ or $C: 30-T=3 a$ ...(ii)
From above two equations $a=2\, m / s ^{2}$