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BITSAT2017PhysicsOscillationsActual

A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ . If it is given a vertical displacement from equilibrium, it undergoes oscillation with a time period T . Then

Options

  1. AT ∝ ρ
  2. BT ∝ 1 A
  3. CT ∝ 1 ρ
  4. DT ∝ 1 m

Correct answer

B. T ∝ 1 A

Step-by-step solution

Let block is displaced through x   m , then weight of displaced water or upthrust (upwards) = - A x ρ g Where, A is area of a cross-section of the block and is density. This must be equal to force = m a applied where m is mass of the block and a is acceleration. ∴   m a = - A x ρ g or a = - A ρ g m x = - ω 2 x This is equation of SHM . The time period of oscillation, T = 2 π ω = 2 π m A ρ g ⇒   T ∝ 1 A

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