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+### Statement
+
+$21.$ ### Problem Statement
+
+$4.2.21^*.$
+
+a. A wooden cylinder with a radius of $1\mathrm{~m}$ and a height of $0.2 \mathrm{~m}$ rises to the surface from a depth of $1$ m in a body of water. The density of the wood is $0.8 \cdot 10^3 \mathrm{~kg/m^3}$. How much heat will be released by the end of the motion of the water and the cylinder?
+
+b*. A cylindrical plug with a radius of $r$ and a height of $h$ falls into a cylinder with a radius of $R$, partially filled with liquid. The initial height of the lower surface of the plug above the liquid level is $H$, and the initial velocity is zero. How much heat will be released by the end of the motion of the liquid and the plug? The density of the plug is $\rho$, and the density of the liquid is $\rho_0 > \rho$.
+
+### Solution
+
+![|1225x1600, 70%](../../img/4.2.21/scan-0.png)
+
+![|1351x1286, 70%](../../img/4.2.21/scan-1.png)
+
+#### Answer
+
+$$
+\mathrm{a.~}Q=1\mathrm{~kJ.~b}^*.Q=\pi r^2\rho ghH\left[1+\frac{1}{2}\frac{h}{H}\frac{\rho}{\rho_0}\left(1-\frac{r^2}{R^2}\right)\right].
+$$
+
+### Solution
+
+[Your solution should be placed here]
+
+#### Answer
+
+[Insert a concise answer or boxed result]