$A$ $U$-tube of small and uniform cross-section contains water of total length $4H$. The height difference between the water columns on the left and on the right is $H$ when the valve $K$ is closed. The valve is suddenly opened,and water flows from left to right. Ignore friction. The speed of the water when the heights of the left and the right water columns are the same is:

  • A
    $\frac{1}{4}\sqrt{gH}$
  • B
    $\sqrt{\frac{gH}{8}}$
  • C
    $\frac{1}{2}\sqrt{gH}$
  • D
    $\sqrt{\frac{gH}{2}}$

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$A.$ Surface tension arises due to extra energy of the molecules at the surface as compared to the molecules in the interior of a liquid.
$B.$ As the temperature of a liquid rises, the coefficient of viscosity increases.
$C.$ As the temperature of a gas increases, the coefficient of viscosity increases.
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$E.$ In a steady flow, two streamlines never intersect.
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$A$ liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in the figure. During rotation, the liquid rises along its sides. If the radius of the vessel is $0.05 \,m$ and the speed of rotation is $10 \,rad \,s^{-1}$, then the height difference between the liquid at the centre of the vessel and its sides is $\left(g=10 \,m \,s^{-2}\right)$.

The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $A$ and top area $a$,and the walls of the vessel are inclined at an angle $30^o$ with the vertical. $A$ liquid of density $\rho$ fills both the sections up to a height $2h$. Neglecting atmospheric pressure:

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The phenomenon of lowering the freezing point of water by the application of pressure is known as

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