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

Question

Infinity Learn · Accepted Answer

If the level of liquid is depressed by cm on one side, then the level of liquid in column P is $$2y$$ cm higher than B as shown.The weight of extra liquid on the side P $$=$$ $$2Aydg$$.This becomes the restoring force on mass M.∴ Restoring acceleration $$=$$ $$-2AydgMThis$$ relation satisfies the condition of SHM i.e., a∝$$-y$$.Hence time periodT $$=$$ $$2$$$$π$$DisplacementAcceleration    $$=$$ $$2$$$$π$$$$y2AydgM$$   ⇒ T $$=$$ $$2$$$$π$$$$M2Adg$$

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

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