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A cylidrical wooden piece of cork floats...

A cylidrical wooden piece of cork floats in a liquid of density `sigma`. The cork is depressed slightly and released. Show that the cork will oscillate up and down simple harmonicaly with a period.
`T=2pisqrt((rhoh)/(sigmag))`, where `rho` is the density of the cork.

Answer

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A cylindrical piece of cork of base area A and height h floats in a liquid of density rho_(1) . The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period T=2pisqrt((hrho)/(rho_(1)g))

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Knowledge Check

  • A solid cube of side a and density rho_(0) floats on the surface of a liquid of density rho . If the cube is slightly pushed downward, then it oscillates simple harmonically with a period of

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    C
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  • A cylindrical of wood (density = 600 kg m^(-3) ) of base area 30 cm^(2) and height 54 cm , floats in a liquid of density 900 kg^(-3) The block is deapressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :

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    D
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  • A wooden cube (density of wood 'd' ) of side 'l' flotes in a liquid of density 'rho' with its upper and lower surfaces horizonta. If the cube is pushed slightly down and released, it performs simple harmonic motion of period 'T' . Then, 'T' is equal to :-

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    B
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