A uniform cylinder of mass 5 kg, radius 10cm and height 30cm is floating in water with its axis vertical. If the cylinder is displaced from its equilibrium position,

Engineering

Physics

Basics of Simple Harmonic Motion

Liquid Pressure

Buoyancy

Question

A uniform cylinder of mass 5 kg, radius 10cm and height 30cm is floating in water with its axis vertical. If the cylinder is displaced from its equilibrium position,

it will execute SHM if it is displaced vertically by a small distance.

it will execute periodic motion if it is displaced vertically by a small distance.

it will execute SHM if it is displaced horizontally by a small distance.

None of these

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A floating cylinder in water with vertical axis experiences buoyant force equal to weight at equilibrium. When displaced vertically by small distance Δy, buoyant force changes by ρgAΔy (A = cross-sectional area). This creates restoring force F = -ρgAΔy.

Equation of motion: $m \frac{d^{2}}{Δ y} = - ρ g A Δ y$

This is SHM with ω² = ρgA/m. Horizontal displacement causes no restoring force (center of buoyancy remains aligned with center of gravity).

Final answer: it will execute SHM if it is displaced vertically by a small distance.