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Question 31159
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Simple Harmonic Motion: Floating Cylinder MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Floating CylinderHardQuestion 31159

Question

A cylinder of mass m, area A, density ρ_c floats upright in liquid (density ρ_l). When pushed down by x and released, time period is:
  1. A
    2π√(m/(ρ_l Ag))
    Correct
  2. B
    2π√(ρ_c/(ρ_l g))
  3. C
    2π√(m/g)
  4. D
    2π√(h/g)

Correct answer

2π√(m/(ρ_l Ag))

Explanation

Restoring force = ρ_l × A × x × g. F = −(ρ_l Ag)x → k_eff = ρ_l Ag. T = 2π√(m/k_eff) = 2π√(m/(ρ_l Ag)).

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