Be Careful with Liquid

A Rectangular tank having base $$15\text{ cm} \times 20\text{ cm}$$ is filled with water (density $$\rho = 1000 \text{ kg/m}^3$$) upto $$20\text{ cm}$$ height.

One end of ideal spring of natural length $${h}_{\circ } = 20\text{ cm}$$ and force constant $$K = 280\text{ N/m}$$ is fixed to the bottom of the tank so that the spring remains vertical.

This system is in an elevator moving downwards with acceleration $$a = 2\text{ m/s}^2$$. A cubical block of side $$l = 10\text{ cm}$$ and mass $$m = 2\text{ kg}$$ is gently placed over the spring and released gradually.

Find

1. The compression in the spring in the equilibrium position ( in cm) ...Let it be $$a$$.

2. If the block is slightly pushed down from the equilibrium position and released , calculate frequency of its vertical oscillations.

Your answer can be represented as $$\large{ f = \dfrac{b \sqrt{c}}{\pi} \text{ per second}}$$.

, where $$b$$ , $$c$$ are positive integers and $$c$$ is a square free integer.

Enter your answer as $$a \times b \times c$$

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