Answer to Question #300163 in Mechanics | Relativity for prince

Question

If the density of the heavy liquid is 9.1 g/cm3 , by what height h1 does the heavy liquid rise in the left arm? 1. 0.810883 2. 0.435573 3. 0.39233 4. 0.573983 5. 0.459748 6. 0.544456 7. 0.710862 8. 0.899009 9. 0.641132 10. 0.538315

Answer 1

The density of a substance is given by

$\rho=\frac{m}{V}$

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where

m is the mass of the substance

V is its volume

For a liquid in a tube, the volume can be written as

V=AL

where

A is the cross-sectional area of the tube

L is the length of the column of liquid

Therefore the formula can be rewritten as

$\rho = \frac{m}{AL}$

For the light liquid in the right arm of the tube, we have:

m = 92 g (mass)

$\rho$ =1.7 g/cm^3

 (density)

A=4.29cm2

 (cross-sectional area)

Therefore we can re-arrange the equation to find L, the height of the column of light liquid:

$L=\frac{m}{A\rho}=\frac{92}{(4.29)(1.7)}=12.6 ~cm.$

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