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A liquid of mass m is set into oscillations in a U-tube of cross section A. Its time period recorded is T, where $T = 2 π \sqrt{\frac{l}{2 g}}$ , here l is the length of liquid column. If the liquid of same mass is set into oscillations in U-tube of cross section $\frac{A}{16},$ if the time period of oscillation in this case is found to be T'. Find the ratio of $\frac{T^{'}}{T}$ .

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answer is 4.

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Detailed Solution

$Mass is constant \Rightarrow volume density = constant \Rightarrow V_{1} d = V_{2} d$

$\begin{array}{l} (Al) d = [\frac{A}{16} l^{'}] d \Rightarrow l^{'} = 16 l ∵ T = 2 π \sqrt{\frac{l}{2 g}} \\ \Rightarrow \frac{T^{'}}{T} = \sqrt{\frac{l^{'}}{l}} = \sqrt{\frac{16 l}{l}} = 4 \end{array}$

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