The same spring is attached to $2 \ kg, 3 \ kg$ and $1 \ kg$ blocks in three different cases as shown in the figure. If $x_1, x_2$ and $x_3$ are the extensions in the spring in these cases,respectively,find the correct relation between them.

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. $A$ force $F$ applied on the upper string produces an acceleration of $2\,m/s^2$ in the upward direction in both the blocks. If $T$ and $T'$ are the tensions in the two parts of the string,then $T$ and $T'$ are:

Two bodies of mass $4\,kg$ and $6\,kg$ are attached to the ends of a string passing over a pulley. The $4\,kg$ mass is also attached to the ground by another string. The tension $T_1$ in this lower string is equal to ......... $N$ (Take $g = 9.8\,m/s^2$)

If the system of blocks shown in the figure is released from rest, the ratio of the tensions $T_1$ and $T_2$ is (Neglect the mass of the string shown in the figure).

Two blocks of mass $M$ and $m$ are kept on a trolley of mass $M_0$ as shown in the figure. All surfaces are smooth. Select the correct statement.

Two masses $2 \, kg$ and $3 \, kg$ are attached to the ends of a string passed over a pulley fixed at the top. The tension and acceleration are: