| 1 The atmospheric pressure is neglected or explicitly used throughout the solution | 0.10 |
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2
The equilibrium of the piston when spring is undeformed is described: $$\rho_1 gh_1 S=\rho_2 gh_2 S;$$ |
0.20 |
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3
The equilibrium of the piston when the liqiud of density $\rho_1$ is added is described: $$\rho_1 gH_1 S=\rho_2 gH_2 S+kx.$$ |
0.40 |
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| 4 It is noticed that the change of the liquid level in the right limb should be equial to $x$. | 0.30 |
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5
Answer $$k=(\rho_1-\rho_2)gS.$$ |
0.50 |
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1
The equilibrium of the piston when the liqiud of density $\rho_2$ is added is described: $$\rho_1 g(h_1-x)S+\rho_2 gzS=\rho_2 g(h_2+x)S+kx.$$ |
0.40 |
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| 2 The height of the segment of the liquid with density $\rho_2$ is determined. | 0.30 |
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| 3 The shift $x$ of the piston is determined: $$x=\frac{\rho_2 \Delta h}{2(\rho_1-\rho_2)}.$$ | 0.40 |
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4
Answer $$\Delta V=\dfrac{\rho_1 \Delta hS}{\rho_1-\rho_2}$$ |
0.40 |
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