Three blocks of masses $m$, $2m$, and $3m$ are pushed with a force $F$ across a frictionless table as shown in the figure. Let $N_{1}$ be the contact force between the left two blocks ($m$ and $2m$) and $N_{2}$ be the contact force between the right two blocks ($2m$ and $3m$). Then:

$A$ block of mass $M$ is kept on a platform which starts accelerating upwards from rest with a constant acceleration $a$. During the time interval $T$,the work done by the contact force on mass $M$ is

$A$ body of mass $2 \, kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) \, N$. It starts from rest and was at the origin initially. After $4 \, s$,its new coordinates are $(8, b, 20)$. The value of $b$ is ........ . (Round off to the Nearest Integer)

The tension in the string connecting the blocks as shown in the figure is ............ $N$.

An elevator weighing $6000\,kg$ is pulled upward by a cable with an acceleration of $5\,ms^{-2}$. Taking $g$ to be $10\,ms^{-2}$,the tension in the cable is ............ $N$.

$A$ 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 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