Motion of an oscillating liquid column in a U-tube is

Imagine a u-tube having water to a certain level equal on both the sides. Now if the force F is applied on the one side of the u-tube compressing the liquid by and raising the liquid in by in the oher arm.

Thus, the restoring force due to the change in height is given by,

Where is density of the liquid and is the area of cross section.

Thus force is proportional to

Thus, it is a simple harmonic motion.

But

Where height is h

We see that time period is independent of density of liquid.

Thus, option (c) is correct.