# Be Careful with Liquid

**Classical Mechanics**Level 5

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

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

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 \( a \times b \times c\)