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:

$A$ bar of mass $m$ resting on a smooth horizontal plane starts moving due to a constant force $F$. In the process of its rectilinear motion,the angle $\theta$ between the direction of this force and the horizontal varies as $\theta = k x$,where $k$ is a constant and $x$ is the distance traversed by the bar from its initial position. The velocity $(v)$ of the bar as a function of the angle $\theta$ is

The figure shows three blocks in contact and kept on a smooth horizontal surface. What is the ratio of the force exerted by block $A$ on $B$ to that of $B$ on $C$?

$A$ constant horizontal force $\overrightarrow{F}$ of magnitude $10 \,N$ is applied to a block $A$ and this produces an acceleration of magnitude $20 \,m/s^2$. If this block $A$ is then kept against another block $B$ of mass $1.5 \,kg$ as shown in the figure and a force $F^{\prime}$ of $20 \,N$ is applied, find the force on the block $B$. Neglect friction. (in $N$)

The mass of a lift is $2000 \, kg$. When the tension in the supporting cable is $28000 \, N$,then its acceleration is:

$A$ mass $1\, kg$ is suspended by a thread. It is
$(i)$ lifted up with an acceleration $4.9\, m/s^2$
$(ii)$ lowered with an acceleration $4.9\, m/s^2$.
The ratio of the tensions is