A cubical block of side length L has a density Dc and floats in a liquid of dens

Question

A cubical block of side length L has a density Dc and floats in a liquid of density Dl with a small part of the block above the liquid's surface.  Please derive the following in terms of these parameters and constants:

a) Determine the fraction of the volume of the block that is below the liquid's surface.  

b) The block is now pushed downward with a small displacement x and released from rest.  Show that the resulting motion of the block is simple harmonic and determine the period of oscillation.

Please show steps and a drawing to illustrate.  MANY THANKS for helping quickly.

Explanation / Answer

a) A*L1*DL*g =A*L*DC*g

therefore fraction of volume = DC/DL

A = surface area of cube

b)net external force acting = A[(L1+x)DL*g - (L1)DL*g]= A*DL*g*x

accleration = A*DL*g*x / (A*DC*L) = DL*x*g /(DC*L)

ass a = kx theref ore it is simple harmonics and

therefore the time = 2*pi*sqrt(DC*L/(DL*g))

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