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MHT CET20243 May 2024Morning ShiftPhysicsOscillationsActual

A tube of uniform bore of cross-sectional area ' A ' has been set up vertically with open end 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 ', which is equal to [ g = acceleration due to gravity]

Options

  1. A2 MA gd
  2. B2 M 2 Adg
  3. C2 M g
  4. D2 M g d A

Correct answer

B. 2 M 2 Adg

Step-by-step solution

For a depression of y cm on one side, the level of liquid will be 2 y cm higher on the other side. Weight of extra liquid on the P -side =2 Aydg The above weight acts as the restoring force acting on mass M . Restoring acceleration =- 2 Aydg M (- ve sign indicates the acceleration and force are opposite to each other) ... (i) We know for simple harmonic motion, a=- ( k m ) x Comparing (i) and (ii), we see the motion is simple harmonic. aligned T & =2 Displacement Acceleration =2 y 2 Aydg M & =2 M 2 Adg aligned

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