A) \[\sqrt{\frac{A{{a}_{0}}gI}{2}}\]
B) \[\sqrt{\frac{{{a}_{0}}I}{g}}\]
C) \[\frac{A{{a}_{0}}g}{{{I}^{2}}}\]
D) \[\frac{{{a}_{0}}I}{g}\]
Correct Answer: D
Solution :
The diameter of circular part of U-tube is \[l\]. This means the distance between vertical arms of U-tube is \[l\]. Suppose, the atmospheric pressure is\[{{p}_{a}}.\] Since, U-tube is accelerated horizontally. So, inertia force will be experienced in horizontal direction. As, net force = ma, gives \[{{p}_{a}}A+Al\times \rho \times {{a}_{0}}\] \[={{p}_{a}}A+\rho gh\times A\] where, A = area of x-section of tube. and \[\rho \]= density. \[\Rightarrow \] \[hg={{a}_{0}}l\] \[\Rightarrow \] \[h=\frac{{{a}_{0}}l}{g}\]
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