A liquid X of density 3.36 , g/cm^3 is poured | vedclass

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Question

(A) Let the density of liquid $X$ be $\rho_X = 3.36 \, g/cm^3$, the density of liquid $Y$ be $\rho_Y$, and the density of mercury be $\rho_{Hg} = 13.6

Vedclass · Accepted Answer

$0.8$

Vedclass · Answer

(A) Let the density of liquid $X$ be $ho_X = 3.36 \, g/cm^3$, the density of liquid $Y$ be $ho_Y$, and the density of mercury be $ho_{Hg} = 13.6 \, g/cm^3$.At the same horizontal level in a continuous static fluid, the pressure is equal.Let the common interface level be the reference level. In the right arm, the pressure at this level is due to the column of liquid $X$ of height $h_X = 10 \, cm$.In the left arm, the pressure at this level is due to the column of liquid $Y$ of height $h_Y = 8 \, cm$ plus the pressure due to the mercury column of height $h_{Hg} = (10 - 8) \, cm = 2 \, cm$.Equating the pressures at this level:$P_{right} = P_{left}$$ho_X g h_X = ho_Y g h_Y + ho_{Hg} g h_{Hg}$$3.36 	imes 10 = ho_Y 	imes 8 + 13.6 	imes 2$$33.6 = 8 ho_Y + 27.2$$8 ho_Y = 33.6 - 27.2$$8 ho_Y = 6.4$$ho_Y = 0.8 \, g/cm^3$.

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