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?

A wooden block of mass $2\; kg$ rests on a soft horizontal floor. When an iron cylinder of mass $25\; kg$ is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of $0.1\; m /s^2$. What is the action of the block on the floor $(a)$ before and $(b)$ after the floor yields ? Take $g = 10 \;m /s^2$. Identify the action-reaction pairs in the problem

Two masses $M_1$ and $M_2$ are accelerated uniformly on a frictionless surface as shown in figure. The ratio of the tensions $T_1/T_2$ is 

A frictionless cart $A$ of mass $100\  kg$ carries other two frictionless carts $B$ and $C$ having masses $8\  kg$ and $4\  kg$ respectively connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart so that smaller cart do not move relative to  it .......... $N$

On a smooth plane surface (figure) two block $A$ and $B$ are accelerated up by applying a force $15\, N$ on $A$. If mass of $B$ is twice that of $A$, the force on $B$ is  ........... $N$

A block of mass $M$ is at rest on a plane surface inclined at an angle $\theta$ to the horizontal. The magnitude of force exerted by the plane on the block is