$A$ block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $M/2$. If a force $2Mg$ is applied at one end of the rope,the force which the rope exerts on the block 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).

$A$ painter is applying force himself to raise him and the box with an acceleration of $5\, m/s^2$ by a massless rope and pulley arrangement as shown in the figure. The mass of the painter is $100\, kg$ and that of the box is $50\, kg$. If $g = 10\, m/s^2$,then:

$A$ 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

In the figure,the tension in the diagonal string is $60\,N$. Find the magnitude of the horizontal forces $F_1$ and $F_3$ that must be applied to hold the system in the position shown.

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: