A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $\theta=45^{\circ} . P_1$ and $P_2$ are pressures at points 1 and 2, respectively, located at the base of the tube. Let $\beta=\left(\mathrm{P}_1-\mathrm{P}_2\right) /(\rho \mathrm{gd})$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement(s) is (are) correct?
Select ALL correct options:
A
$\beta=0$ when $a=g / \sqrt{2}$
B
$\beta>0$ when $a=g / \sqrt{2}$
C
$\beta=\frac{\sqrt{2}-1}{\sqrt{2}}$ when $a=g / 2$
D
$\beta=\frac{1}{\sqrt{2}}$ when $\mathrm{a}=\mathrm{g} / 2$
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