Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A U-tube is of non uniform cross-section. The area of cross-sections of two sides of tube are $A$ and $2 A$ (see fig.). It contains non-viscous liquid of mass $m$. The liquid is displaced slightly and free to oscillate. Its time period of oscillations isPhysics Question Image

MHT CETMHT CET 2020

Solution:

Suppose the liquid in left side limb is displaced slightly by $y$,
the liquid in right limb will increase by $y / 2$.
The restoring force
$F =-P A $
$=-\rho g\left(\frac{3 y}{2}\right) \times 2 A=3 \rho g A(-y) .$
$a =\frac{F}{m}=3 \rho g A(-y) / m$
image
On comparing with, $a=-\omega^{2} y$, we get
$\omega=\sqrt{\frac{3 \rho g A}{m}}$ and
$T=2 \pi \sqrt{\frac{m}{3 \rho g A}}$