A cylindrical plastic bottle of negligible mass is filled with 310   m l of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω . If the radius of the bottle is 2.5   c m then ω is close to: ( density of water = 10 3 k g / m 3 )

Step-by-step solution

Let at equilibrium, y length of bottle is immerged in water: So, m g = f b u o m g = ρ A y g ..... ( 1 ) [Equilibrium Condition] Now it is further pushed by distance x F r e s t o r i n g = ρ [ A x + y ) g - m g m ω 2 x = ρ A x g + ρ A y g - m g ω = ρ A g m = ρ A g ρ V = π r 2 g V =7.9   r a d / s e c