(C) Let the initial height of water in each arm be $H = 20 \text{ cm}$. The total volume of water remains constant. When the immiscible liquid is adde

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(C) Let the initial height of water in each arm be $H = 20 \text{ cm}$. The total volume of water remains constant. When the immiscible liquid is added,the water level in one arm drops by $x$ and rises in the other arm by $x$.Thus,$h_1 = H - x + 5 = 20 - x + 5 = 25 - x$ and $h_2 = H + x = 20 + x$.Equating the pressure at the bottom of the $U$-tube:$P_{\text{left}} = P_{\text{right}}$$5 \times 4 \times g + (h_1 - 5) \times 1 \times g = h_2 \times 1 \times g$$20 + (25 - x - 5) = 20 + x$$20 + 20 - x = 20 + x$$2x = 20 \Rightarrow x = 10 \text{ cm}$.Now,$h_1 = 25 - 10 = 15 \text{ cm}$ and $h_2 = 20 + 10 = 30 \text{ cm}$.The ratio $h_2/h_1 = 30/15 = 2/1$.

Class 11 Physics Mechanical Properties of Fluids Pressure and Density (of Mixure)

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An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \text{ g/cm}^3$) standing initially $20 \text{ cm}$ from the bottom in each arm. An immiscible liquid of density $4.0 \text{ g/cm}^3$ is added to one arm until a layer $5 \text{ cm}$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

A
$3/1$
B
$5/2$
C
$2/1$
D
$3/2$

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Mechanical Properties of Fluids

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Pressure and Density (of Mixure)

$A$ liquid $X$ of density $3.36 \ g/cm^3$ is poured into a $U$-tube, which contains $Hg$. Another liquid $Y$ is poured into the left arm with a height of $8 \ cm$. The upper levels of $X$ and $Y$ are at the same height. What is the density of $Y$ in $g/cc$?

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$A$ uniform long tube is bent into a circle of radius $R$ and it lies in a vertical plane. Two liquids of the same volume but densities $\rho$ and $\delta$ fill half the tube. The angle $\theta$ is

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The figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on a vertical line,and points $B$ and $D$ lie on a horizontal line. Which of the following statements is incorrect? (Here,$p_A, p_B, p_C, p_D$ are the absolute pressures at the respective points.)

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$A$ hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. The sphere is moving horizontally with an acceleration $2g,$ where $g$ is the acceleration due to gravity. If the minimum pressure of the liquid is $P_0$,then what is the pressure at the centre of the sphere?

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Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_A, \rho_B$ and $\rho_C$ (where $\rho_A > \rho_B > \rho_C$). The pressure at the bottom of the vessels is:

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$A$ liquid $X$ of density $3.36 \ g/cm^3$ is poured into a $U$-tube, which contains $Hg$. Another liquid $Y$ is poured into the left arm with a height of $8 \ cm$. The upper levels of $X$ and $Y$ are at the same height. What is the density of $Y$ in $g/cc$?

$A$ uniform long tube is bent into a circle of radius $R$ and it lies in a vertical plane. Two liquids of the same volume but densities $\rho$ and $\delta$ fill half the tube. The angle $\theta$ is

Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_A, \rho_B$ and $\rho_C$ (where $\rho_A > \rho_B > \rho_C$). The pressure at the bottom of the vessels is:

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