Two blocks of masses $7 \, kg$ and $5 \, kg$ are placed in contact with each other on a smooth surface. If a force of $6 \, N$ is applied on the heavier mass,the force on the lighter mass is ............ $N$.

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface as shown in the figure. The tension in the string will be

$A$ 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

Two blocks of mass $8\,kg$ and $2\,kg$ are connected by a string and they are released on an inclined plane of inclination $30^o$ as shown in the figure. What will be the tension in the string connecting the two blocks (in $,N$)? (Assume the surface is frictionless and $g = 10\,m/s^2$)

$A$ freely falling body has attained a velocity of $2 \,m/s$. If the weight of the body is now opposed by a constant upward air resistance force equal to its weight, what is the total distance travelled by the body before it comes to rest (in $\,m$)?

The arrangement of a two-block system is as shown. Assuming the surfaces to be frictionless,the net force acting on the $1 \, kg$ and $2 \, kg$ blocks are,respectively: