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MHT CET 2024 (3 May, Shift 1) · Other SHM Systems

Other SHM Systems question from MHT CET 2024 (3 May, Shift 1)

Q12MHT CET 2024 · 3 MAY · SHIFT 1Medium

Other SHM Systems

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]

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Answer: (b)

Treat it as a U-tube: displacing the liquid by $x$ makes a level difference $2x$ , restoring force $2Adgx$ .
$T = 2\pi\sqrt{\frac{M}{2Adg}}$ (equivalently $2\pi\sqrt{\frac{L}{2g}}$ with column length $L = \frac{M}{Ad}$ ).
So the answer is (b).

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