In the given arrangement all surfaces are smooth. What acceleration should be given to the system, for which the block $m_2$ doesn't slide down?

Three solids of masses ${m_1},\,{m_2}$ and ${m_3}$ are connected with weightless string in succession and are placed on a frictionless table. If the mass ${m_3}$ is dragged with a force T, the tension in the string between ${m_2}$ and ${m_3}$ is

Consider the shown arrangement. Assume all surfaces to be smooth. If $N$ represents magnitudes of normal reaction between block and wedge, then acceleration of $M$ along horizontal equals

Two blocks $'A$' and $'B'$ each of mass $'m'$ are placed on a smooth horizontal surface. Two horizontal force $F$ and $2F$ are applied on the $2$ blocks $'A'$ and $'B'$ respectively as shown in figure. The block $A$ does not slide on block $B$. Then the normal reaction acting between the two blocks is

Three blocks of masses $4\, kg, 8\,kg$ and $24 \,kg$ are connected to each other with  light strings and placed on a smooth horizontal floor as shown in figure. If the system  moves with an acceleration of $2\, ms^{-2}$, the applied force $F$ is ............ $N$

Two blocks of mass $8\,kg$ and $2\,kg$ are connected by a string and they are released on  a inclined plane of inclination $30^o$ as shown in figure then what will be the tension  in string connecting the two blocks  ............ $N$