Three blocks $A, B$ and $C,$ of masses $4\, kg, \,2 \,kg$ and $1\, kg$ respectively, are in contact on a frictionless surface, as shown. If a force of $14\, N$ is applied on the $4 \,kg$ block, then the contact force between $A$ and $B$ is  .......... $N$

A wooden block of mass $5 \mathrm{~kg}$ rests on soft horizontal floor. When an iron cylinder of mass $25$ $\mathrm{kg}$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1 \mathrm{~ms}^{-2}$. The action force of the system on the floor is equal to:

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 $1$) and $T'$ be the tension when it is applied to $B$ (figure $2$), then which of the following is true

Three masses $M =100\,kg , m _{1}=10\,kg$ and $m_{2}=20\,kg$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. $A$ force $F$ is applied on the system so that the mass $m_{2}$ moves upward with an acceleration of $2\,ms ^{-2}$. The value of $F$ is $......N$

$\left(\right.$ Take $\left.g =10\,ms ^{-2}\right)$

A block of mass $m$ slides down on a wedge of mass $M$ as shown in figure. Let $\vec a_1$ be the acceleration of the wedge and $\vec a_2$  the acceleration of block w.r.t. ground. $N_1$ is the normal reaction between block and wedge and $N_2$ the normal reaction between wedge and ground. Friction is absent everywhere. Select the incorrect alternative