Two blocks of masses $m$ and $2m$ are connected by a metal wire of negligible mass and having cross-sectional area $A$,passing over a smooth fixed pulley as shown in the figure. If the masses are released from rest,then the stress produced in the wire is:

$A$ light string passes over a frictionless pulley. To one of its ends a mass of $6\, kg$ is attached. To its other end a mass of $10\, kg$ is attached. The tension in the thread will be ........ $N$.

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 $(g = 10 \, m/s^2)$ ......... $m/s$.

Three masses $m_1 = 4 \text{ kg}$, $m_2 = 4 \text{ kg}$, and $m_3 = 6 \text{ kg}$ are suspended from a fixed smooth frictionless pulley as shown in the figure. The value of $T_1/T_2$ is . . . . . . . (Take $g = 10 \text{ m/s}^2$)

For the system shown in the figure,$m_1 > m_2 > m_3 > m_4$. Initially,the system is at rest in equilibrium. If the string joining $m_4$ and the ground is cut,then just after the string is cut:
Statement $I$: $m_1$,$m_2$,and $m_3$ remain stationary.
Statement $II$: The value of acceleration of all the $4$ blocks can be determined.
Statement $III$: Only $m_4$ remains stationary.
Statement $IV$: Only $m_4$ accelerates.
Statement $V$: All the four blocks remain stationary.
Now,choose the correct option.

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is: