Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

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.

$\therefore Restoringacceleration=\frac{-2Aydg}{M}$

This relation satisfies the condition of SHM i.e. a $\infty -y$
Hence time period T = $2\pi \sqrt{\frac{Displacementnt}{Acceleration}}$
= $2\pi \sqrt{\frac{y}{\frac{2Aydg}{M}}}\Rightarrow T=2\pi \sqrt{\frac{M}{2Adg}}$