A cylindrical object of outer diameter 20 cm and mass 2 kg floats in water with its axis vertical. If it is slightly depressed and then released, find the time period of the resulting simple harmonic motion of the object.

Explanation

Given d=20`
`rarr r=d/2=10cm`
When depressed downward the net unbalanced force will cause SHM. Let xrarr displacement of the block from the equilibrium positoinso, Driving force `=U=V(rho_ug)`
`rarr ma=pir^2(X)xxrho_ug)`
`a=(pir^2rho_w9x)/(2xx10^3)`
`[because m=2kg=2xx10^3g]`
`T=2pisqrt(displacement/AScceleration)`
`=2pisqrt((x)xx2xx10^3)/((pir^2rho_wg(x)))`
`=2pisqrt(2xx10^3)/(pixx(10)62xx1xx10))`
`=2pisqrt(2/(pixx10))=0.5sec`