Be Careful with Liquid

A rectangular tank having base 15 cm × 20 cm \SI{15}{\centi\meter} \times \SI{20}{\centi\meter} is filled with water (density ρ = 1 000 kg / m 3 \rho = \SI[per-mode=symbol]{1000}{\kilo\gram\per\meter\cubed} ) up to 20 cm \SI{20}{\centi\meter} height. One end of an ideal spring of natural length h 0 = 20 cm h_0 = \SI{20}{\centi\meter} and force constant K = 280 N / m K = \SI[per-mode=symbol]{280}{\newton\per\meter} 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 m / s 2 a = \SI[per-mode=symbol]{2}{\meter\per\second\squared} . A cubical block of side l = 10 cm l = \SI{10}{\centi\meter} and mass m = 2 kg m = \SI{2}{\kilo\gram} is gently placed over the spring and released gradually.

  1. Find the compression a a (in cm \si{\centi\meter} ) in the spring in the equilibrium position.
  2. If the block is slightly pushed down from the equilibrium position and released, find the frequency of oscillation about the equilibrium position f = b c π f = \dfrac {b\sqrt c}\pi (in Hz \si{\hertz} ), where b b and c c are positive integers with c c being square-free.

Enter your answer as a b c abc .


This is a part of my set Aniket's Mechanics Challenges .


The answer is 40.00.

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