Block $A$ of mass $4 \;kg$ is to be kept at rest against a smooth vertical wall by applying a force $F$ as shown in figure. The force required is .......... $N$ $\left(g=10 m / s ^2\right)$

A rope of length $10\, m$ and linear density $0.5\, kg/m$ is lying lengthwise on a smooth horizontal floor. It is pulled by a force of $25\, N$. The tension in the rope at a point $8\, m$ away from the point of application is ....... $N$

There are four forces acting at a point $P$ produced by strings as shown in figure, point $P$ is at rest. The forces $F_1$ and $F_2$ are respectively

A uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$ . The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge ?

Figure shows two cases. In first case a spring (spring constant $K$ ) is pulled by two equal and opposite forces $F$ at both ends and in second case is pulled by a force $F$ at one end. Extensions $(x)$ in the springs will be