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MHT CET Medical202623 April 2026Morning ShiftPhysicsOscillationsActual

The U tube of uniform bore of cross-sectional area A has been set up vertically with open ends facing up. Now M gram of a liquid of density d is poured into it. The column of liquid in this tube will oscillate with a period T. The period is

Options

  1. A2 MA gd
  2. B2 M 2Agd
  3. C2 M g
  4. D2 M gdA

Correct answer

B. 2 M 2Agd

Step-by-step solution

Let the liquid be displaced by a small distance x in one arm of the U-tube. The liquid level in the other arm rises by x , creating a level difference of 2x between the two arms. The restoring force acting on the liquid is due to the weight of this excess liquid column. F = -(2x) A d g The acceleration of the liquid column of mass M is a = F M . a = - ( 2 A d g M ) x Comparing this with the standard equation of simple harmonic motion a = - ^2 x , we get: ^2 = 2 A d g M = 2 A d g M The time period of oscillation is

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