A wooden stick of length L, radius R and density ρ has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value for the mass m (in terms of given parameters) that would make the stick float vertically in stable equilibrium in a liquid of density σ .

Question

A wooden stick of length L, radius R and density ρ has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value for the mass m (in terms of given parameters) that would make the stick float vertically in stable equilibrium in a liquid of density σ ., 2 π R 2 L ρ σ ρ - 1, π R 2 L ρ 2 σ ρ - 1, π R 2 L ρ σ ρ - 1, π R 2 L ρ σ 2 ρ - 1

MARKS App · Accepted Answer

M + m g = π R 2 h σ g .... (i) M = π R 2 L ρ The height of center of mass from bottom M L / 2 + m × 0 m + M = M L 2 m + M For rotatory equilibrium and for minimum m, thus should be equal to h / 2 ∴ h 2 = M L 2 m + M .... (ii) ∴ h = M L 2 m + M ; m = π R 2 L σ ρ - π R 2 L ρ = π R 2 L ρ σ ρ - 1

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