A rigid, uniform, weightless, horizontal bar is connected to three vertical members P , Q and R as shown in the figure (not drawn to the scale). All three members have identical axial stiffness of $10\:kN/mm$ . The lower ends of bars $P$ and $R$  rest on a rigid horizontal surface. When $\textbf{NO}$ load is applied, a gap of $2\:mm$ exists between the lower end of the bar $Q$ and the rigid horizontal surface. When a vertical load $W$ is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displaced by $5\:mm$ in the vertically downward direction.

The magnitude of the load $W$ (in $kN$, round off to the nearest integer), is  ______.