A thin V-shaped glass tube is bent through the right angle and is fixed in the vertical plane as shown. Initially, the left part of the tube contains a column of water of length $d = \sqrt{2} m .$ A valve at the bottom of the tube prevents the water from moving to right part. At some time, the valve is quickly opened. Neglecting friction, find the time (in seconds) it takes for the water to move completely into the right part of the tube. $(T a k e g = π^{2} m / s^{2})$

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Detailed Solution

The water of density $ρ$ will execute SHM inside the fixed v-shape glass tube of
Time period $T = 2 π \sqrt{\frac{m}{2 ρ A g \cos 45 °}}$
where m = mass of water and A = cross-section area of tube.
$∴ T = 2 π \sqrt{\frac{d}{\sqrt{2} g}}$
Hence the required time is half the time period of oscillation.

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