A cylindrical plastic bottle of negligible mass is filled with 310 mL 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 cm then ω close to : (Density of water = 10³ kg m⁻³)
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Question

A cylindrical plastic bottle of negligible mass is filled with 310 mL 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 cm then ω close to : (Density of water = 10³ kg m⁻³)

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G1 Physics · Accepted Answer

Step 1: Apply Archimedes' principle, Fᵦ = ρfluid g Vdisplaced, together with force/torque equilibrium. Step 2: Use the immersed volume from the given geometry and solve the balance condition. Applying these relations to the given data gives D: 2.50 rad s⁻¹. Final answer: D.