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 $N$)

$A$ rope of mass $5 \,kg$ is moving vertically in a vertical position with an upward force of $100 \,N$ acting at the upper end and a downward force of $70 \,N$ acting at the lower end. The tension at the midpoint of the rope is ......... $N$.

For the given figure,what will be the acceleration of the blocks and the tension in the string connecting the $2\,kg$ and $5\,kg$ blocks? (Assume $g = 10\,m/s^2$)

Two bodies $A$ and $B$ of masses $10\, kg$ and $15\, kg$ respectively,kept on a smooth horizontal surface,are tied to the ends of a light string. If $T$ represents the tension in the string when a horizontal force $F = 500\, N$ is applied to $A$ (as shown in figure $I$) and $T'$ is the tension when it is applied to $B$ (figure $II$),then which of the following is true?

$A$ block of mass $m$ slides on a wooden wedge,which in turn slides backward on a horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg, M = 16 \, kg$. Assume all surfaces shown in the figure to be frictionless.

Four blocks are connected as shown in the figure on a horizontal frictionless surface. If $m_1 = m_2 = m_3 = m_4 = m$,then the ratio $T_3 / T_4$ will be: