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))`

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.

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

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) :

A block of ice with an area A and a height h floats in water of density rho_(0) . What work should be performed to submerge the ice block completely into water if density of ice is rho_(1) ?

A plank of mass 'm' and area of cross - section A is floating in a non - viscous liquid of desity rho . When displaced slightly from the mean position, it starts oscillating. Prove that oscillations are simple harmonic and find its time period.

A cylinderical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute S.H.M. with a tiem period. T=2pisqrt((m)/(Arhog) where m is mass of the body and rho is density of the liquid.

A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that lon would execute SHM with a time period. T=2pisqrt((m)/(Apg)) where, m is mass of the body and p is density of the liquid.

A rectangular block of mass m and area of cross-section A floats in a liquid of density rho . If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then