Consider a cylindrical piece of wood of density 0.6 gm/cc. Its radius is 3 cm. a

Question

Consider a cylindrical piece of wood of density 0.6 gm/cc. Its radius is 3 cm. and its length is 2 cm. It is floating undisturbed on a water surface. It is suddenly pushed downwards by 0.5 cm and then let go. Describe its subsequent motion by invoking Archimedes' principle: An object that is completely or partially immersed in a fluid is acted on by an upward force equal to the weight of fluid displaced. The piece of wood bobs up and down. What is the period of the bodies' motion? Answer: 0.22 sec

Explanation / Answer

buoyancy foce = F = pi*r^2*x*d*g

acceleration = a = F/m = pi*r^2*x*d*g/pi*r^2*L*D

acceleration a = (dg/L*D)*x

but acceleraion = a = w^2*x

w = sqrt(dg/LD)

time period = T = 2*pi/w

T = 2*pi*(sqrtLD/dg)

T = 2*pi*sqrt((0.02*600)/(1000*9.8))

T = 0.22 s <<<<<answer

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