A thin uniform rigid bar of Length $L$ and mass $M$ is hinged at point $O$, located at a distance of $\dfrac{L}{3}$ from one of its ends. The bar is further supported using springs, each of stiffness $k$, located at the two ends. A particle of mass $m=\dfrac{M}{4}$ is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about $O$, the natural frequency of the system is
- $\sqrt{\dfrac{5k}{M}} \\$
- $\sqrt{\dfrac{5k}{2M}} \\$
- $\sqrt{\dfrac{3k}{2M}} \\$
- $\sqrt{\dfrac{3k}{M}}$