A uniform cylinder of length L and mass M , having cross-sectional area A is suspended with its length vertical from a fixed point by a massless spring of constant K such that it is half-submerged in

Question

A uniform cylinder of length L and mass M , having cross-sectional area A is suspended with its length vertical from a fixed point by a massless spring of constant K such that it is half-submerged in the liquid of density σ in the equilibrium position. The extension of the spring x 0 in equilibrium position is

TestHub · Accepted Answer

Let x 0 = extension in equilibrium position F = Restoring force in the spring F = K x 0 The net downward force acting on the cylinder = Mg - upward thrust = Mg - L / 2 × A × σ × g For equilibrium Kx o = Mg - LA σ g / 2 Kx o = Mg 1 - LA σ / 2 M x o = Mg / K 1 - LA σ / 2 M

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