A $3 \mathrm{~m}$ long, horizontal, rigid, uniform beam $\mathrm{PQ}$ has negligible mass. The beam is subjected to a $3 \mathrm{kN}$ concentrated vertically downward force at $1 \mathrm{~m}$ from $\mathrm{P}$, as shown in the figure. The beam is resting on vertical linear springs at the ends $\mathrm{P}$ and $\mathrm{Q}$. For the spring at the end $\text{P}$, the spring constant $\text{K}_\text{P}=100 \mathrm{kN} / \mathrm{m}$.
(Figure NOT to scale)
If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant $\text{K}_{Q}$ (in $\mathrm{kN} / \mathrm{m}$ ) for the spring at the end $\mathrm{Q}$ is
- $150$
- $100$
- $50$
- $200$