There is a cylindrical bottle of negligible mass and radius 2.5 c m floating in the water of density 10 3 kg m - 3 filled with 310 m l of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is

Question

There is a cylindrical bottle of negligible mass and radius 2.5 c m floating in the water of density 10 3 kg m - 3 filled with 310 m l of water inside it. Now the bottle is slightly dipped into water and released. The frequency of oscillation is, 3.75 s - 1 ⁡, 1.25 s - 1 ⁡, 2.75 s - 1 ⁡, 3.00 s - 1 ⁡

MARKS App · Accepted Answer

Let at equilibrium, y length of the bottle is immersed 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 = 2 π f ∴ f = 1 2 π π r 2 g V = 1 .25 s - 1

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