Two weights of mass $m_{1}$ and $m_{2} (> m_{1})$ are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is

An arrangement of a spring,strings,a pulley,and masses is shown in the figure below. The pulley and the strings are massless and $M > m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached,then immediately after detachment,

$A$ particle of small mass $m$ is joined to a very heavy body of mass $M$ by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

Three blocks $A, B$ and $C$ are suspended as shown in the figure. The mass of each block $A$ and $C$ is $m$. If the system is in equilibrium and the mass of $B$ is $M$,then:

In the system shown in the figure,there is no friction anywhere. The block $C$ $(2 \, kg)$ moves down by a distance $x_0 = 10 \, cm$ with respect to the wedge $D$ $(4 \, kg)$ when the system is released from rest. The velocity of $A$ $(1 \, kg)$ with respect to $B$ $(1 \, kg)$ will be $(g = 10 \, m/s^2)$ ......... $m/s$.

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2m$,then the stress produced in the wire is