What is the acceleration of $3 \,kg$ mass when acceleration of $2 \,kg$ mass is $2 \,m / s ^2$ as shown is ............... $m / s ^2$

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 .......... $N$

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block will be

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 mass $M$ is placed on a very smooth wedge resting on a surface without friction. Once the mass is released, the acceleration to be given to the wedge so that $M$ remains at rest is $a$ where

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