# Problem No. 7 (15 points)

For a body completely submerged in a liquid to be in equilibrium, a force $F=5 \mathrm{H}$ is applied to it. Determine the density of the body if its volume $V=1$ l, and the density of the liquid $\rho_{\text {ж }}=1000$ kg $/ \mathrm{m}^{3}$.

Answer: $1500 \mathrm{\kappa z} / \boldsymbol{m}^{3}$

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# Solution and Evaluation Criteria:

We need to consider two situations:

The first is when the body tries to float. In this case, the equilibrium condition is:

$F_{a}=m g+F$.

As a result, we get: $\rho_{\text{ж}} g V=\rho_{T} V g+F$
$\rho_{T}=\frac{\rho_{\text{ж}} g V-F}{g V}=\frac{10-5}{10 \cdot 10^{-3}}=500 \mathrm{k} 2 / \mathrm{m}^{3}$

The second is when the body tries to sink. In this case, the equilibrium condition is:

$F_{a}+F=m g$.

(4 points)

As a result, we get: $\rho_{\text{ж}} g V+F=\rho_{T} V g$

$\rho_{T}=\frac{\rho_{\text{ж}} g V+F}{g V}=\frac{10+5}{10 \cdot 10^{-3}}=1500 \mathrm{k} / \mathrm{m}^{3}$