Determine in the given diagram, the acceleration $a$ of the system and the tension $T_1$ and $T_2$ in the strings. Assume that the table and pulleys are frictionless and the strings are massless. $\left(g=9.8 \mathrm{m}/{\mathrm{s}}^2\right)$

 

The figure shows a massless, frictionless pulley hanging by a spring balance. The free ends of a cord passing over the pulley carry $1 \mathrm{kg}$ and $5 \mathrm{kg}$ weights which move under the action of gravity. Will the spring balance read $6 \mathrm{kg}-\mathrm{wt}$ or less than $6 \mathrm{kg}-\mathrm{wt}$ or more than $6 \mathrm{kg}-\mathrm{wt}$ during the motion of the weights?

Two blocks of masses $10 \mathrm{g}$ and $30 \mathrm{g}$ are fastened to the ends of a cord which passes over a frictionless pulley. The $10 \mathrm{g}$ block rests on the table. What minimum force must be applied to the $10 \mathrm{g}$ block to keep it on the table? What will be the tension in the cord under this condition? What will be the acceleration of the system and the tension in the cord when the force is withdrawn?

Two blocks are connected by a string as shown in the figure. The upper block is hung by another string. What will be the tension in the upper string due to the two blocks suspended in rest position?

Two blocks are connected by a string as shown in the figure. The upper block is hung by another string. What force $F$ will have to be applied on the upper string to produce an acceleration of $2 \mathrm{m}/{\mathrm{s}}^2$ in the upward direction in both the blocks?

Two blocks are connected by a string as shown in the figure. The upper block is hung by another string. If force $F$ is applied on the upper string to produce an acceleration of $2 \mathrm{m}/{\mathrm{s}}^2$ in the upward direction in both the blocks then, what will be the tension in the string between the two blocks?

A $70 \mathrm{kg}$ person in the sea is being lifted by a helicopter with the help of a rope which can bear a maximum tension of $100 \mathrm{kg}-\mathrm{wt}$. With what maximum acceleration the helicopter should rise so that the rope may not break? $\left(g=9.8 {\mathrm{ms}}^{-2}\right)$