A wooden cylinder is floating in water with its axis vertical and its submerged length is 10 cm. If it is slightly pushed into water and released, its starts oscillating with time period T. If g = 10 m/s2 find T in second.

When the cylinder is in equilibrium, mg=ρ.A.l.gwhen the submerged length is (l + x), net upward force acting on the cylinder is equal to ρAl+xg−mg=ρAlg−mg+ρAg.x=ρAgx∴ ma=−ρAgx⇒ma=−mlg.x⇒a=−glx∴ ω=gl⇒T=2πω=2πlg=2π0.110 S=π5sec