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 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

A block of mass $200\, g$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F =\sqrt{ x }N$ as shown in figure. The value of $x =.....$

For frictionless surfaces in given arrangement tension $T_2$ 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 .......... $N$

Three blocks with masses $m, 2m $ and $3 m$ are connected by strings, as shown in the figure. After an upward force $F$ is applied on block $m,$ the masses move upward at constant speed $v.$ What is the net force on the block of mass $2\ m\ ?\, (g$ is the acceleration due to gravity$)$