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 trolley is falling freely on inclined plane as shown in the figure. The angle of string of pendulum with the ceiling of trolley is $(\alpha)$ equal to ..........

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively

A man of mass $50 \,kg$ carries a bag of weight $40 \,N$ on his shoulder. The force with which the floor pushes up his feet will be ......... $N$

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

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