In the system shown in the figure,the acceleration of the $1\,kg$ mass and the tension in the string connecting between $A$ and $B$ is

Two masses of $5\, kg$ and $10\, kg$ are connected to a pulley as shown. What will be the acceleration of the system if the pulley is set free? ($g =$ acceleration due to gravity)

If $m_1 = 4m_2$,and the acceleration of $m_1$ is $a$,then find $a$.

In order to test the strength of a rope,one end is tied to a large tree and the other end is hitched to a team of $2$ horses. The horses pull as hard as they can,but cannot break the rope. If the rope is untied from the tree and attached to another team of $2$ horses with equal strength,and the two teams pull in opposite directions,the tension in the rope will

$A$ $2 \, kg$ block is lying on a smooth table and is connected to a body of mass $1 \, kg$ by a string passing over a pulley. The $1 \, kg$ mass is hanging vertically. Find the acceleration of the block and the tension in the string.

Two blocks $A$ and $B$,each of the same mass,are attached by a thin inextensible string through an ideal pulley. Initially,block $B$ is held in position as shown in the figure. Now,block $B$ is released. Block $A$ will slide to the right and hit the pulley in time $t_A$. Block $B$ will swing and hit the surface in time $t_B$. Assume the surface is frictionless. [Hint: Tension $T$ in the string acting on both blocks is the same in magnitude. Acceleration needed for horizontal motion is provided by $T$.]