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Icicle on thread

B1  1.00 Determine the initial temperature $t_1$ of the ball if the icicle stopped descending when the ball had melted a hole of depth $H=10~\text{cm}$.

1 Thermal balance is written:
\[ C(t_1 - t_0) = \lambda \rho S H\]
0.40
2 \[t_1 = t_0 + \frac{\lambda \rho S H}{C} \] 0.30
3 \[t_1 = 100^\circ\text{C}\] 0.30
B2  2.00 At the moment when the icicle had descended by $2H/3$ its velocity was $v_2 = 0.1~\text{mm}/\text{s}$. Determine the velocity $v_0$ of the icicle at the initial stage of the experiment.

1 Thermal balance is written:
\[ \alpha (t-t_0) = \lambda \rho S v\]
0.50
2 It's written that
\[ \frac{t_2-t_0}{t_1 - t_0} = \frac{v_2}{v_0} \]or
\[\alpha = 0.0594~\text{W}/^\circ\text{C}\]
0.20
3 Thermal balance is written:
\[ C (t_1-t) = \lambda \rho S h\]
0.40
4 \[ \frac{t_1-t}{t_1 - t_0} = \frac{h}{H} \] 0.10
5 It's obtained
\[t_2 = t_1 - \frac{2}{3} (t_1 - t_0) = 33.3^\circ\text{C}\]
0.30
6 \[v_0 = 3 v_2 \] 0.30
7 \[v_0 = 0.3~\text{mm}/\text{s}\] 0.20