$A$ block $A$ of mass $7 \, kg$ is placed on a frictionless table. $A$ thread tied to it passes over a frictionless pulley and carries a body $B$ of mass $3 \, kg$ at the other end. The acceleration of the system is .......... $m \, s^{-2}$ (given $g = 10 \, m \, s^{-2}$).

Three blocks are connected as shown in the figure on a horizontal frictionless table. If $m_1 = 1 \, kg, m_2 = 8 \, kg, m_3 = 27 \, kg$ and $T_3 = 36 \, N$,then $T_2$ will be ............ $N$.

Three masses of $16 \, kg$,$8 \, kg$,and $4 \, kg$ are placed in contact as shown in the figure. If a force of $140 \, N$ is applied on the $4 \, kg$ mass,then the force on the $16 \, kg$ mass will be ............ $N$.

$A$ small block of mass $m$ is placed on a wedge of mass $M$ as shown,which is initially at rest. All the surfaces are frictionless. The spring attached to the other end of the wedge has a force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down,then the maximum velocity of $M$ is:

Three blocks of masses $4 \ kg$, $2 \ kg$, and $1 \ kg$ respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \ N$ is applied on the $4 \ kg$ block, the contact force between the $4 \ kg$ and the $2 \ kg$ block will be: (in $N$)

Two blocks of mass $M_1 = 20\,kg$ and $M_2 = 12\,kg$ are connected by a metal rod of mass $8\,kg$. The system is pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is ........ $N$.