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 y 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  $$=$$− $$2AydgM$$ This relation satisfies the condition of SHM i.e. a∝−y. Hence time period $$T=2$$$$π$$Displacement|Acceleration|   $$=2$$$$π$$$$y2AydgM$$⇒$$T=2$$$$π$$$$M2Adg$$

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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