Two blocks of masses $1\,kg$ and $5\,kg$ are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a spring balance as shown in the figure. The blocks start moving; during this interval,the reading of the spring balance will be:

$A$ lift of mass $1000\,kg$ is moving with an acceleration of $1\,m/s^2$ in the upward direction. The tension developed in the cable connected to the lift is ........... $N$ $(g = 9.8\,m/s^2)$.

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 $T$.]

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

The acceleration of the $2\,kg$ block if the free end of the string is pulled with a force of $20\,N$ as shown in the figure is:

$A$ mass of $10 \; kg$ is suspended by a rope of length $4 \; m$ from the ceiling. $A$ force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then $F$ equals ........... $N$ (Take $g = 10 \; ms^{-2}$ and the rope to be massless).