水平地面上有底面积为$300\text{c}\text{m}^2$、不计质量的薄壁盛水柱形容器$\;A$,内有质量为$400\text{g}$、边长为$10\text{cm}$,质量分布均匀的正方体物块$\;B$,通过一根长$10\text{cm}$的细线与容器底部相连,此时水面 距容器底$30\text{cm}$(如图甲),计算可得出( )
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A.木块的重力:$G = mg = 0.4\text{kg} \times 10\text{N/kg} = 4\text{N}$,$V_排 = V_木 = (10\text{c}\text{m}^3) = 1 \times 10^{- 3}\text{m}^3$,
$F_浮 = \rho _水gV_排 = 1.0 \times 10^3\text{kg/}\text{m}^3 \times 10\text{N/kg} \times 1 \times 10^{- 3}\text{m}^3 = 10\text{N}$,
绳子的拉力为:$F = F_浮 - G = 10\text{N} - 4\text{N} = 6\text{N}$,故A错误;
B.容器内水的体积:$V = Sh = 300\text{c}\text{m}^2 \times 30\text{cm} - 1000\text{c}\text{m}^3 = 8000\text{c}\text{m}^3 = 8 \times 10^{- 3}\text{m}^3$,
由$\rho = \frac {m}{V}$可知,水的质量$m_水 = \rho V = 1.0 \times 10^3\text{kg/}\text{m}^3 \times 8 \times 10^{- 3}\text{m}^3 = 8\text{kg}$,
不计质量的薄壁盛水柱形容器,则容器对水平地面的压力$F = G_总 = (m_水m_B) = (0.4\text{kg} + 8\text{kg}) \times 10\text{N/kg = 84N}$,
故B正确;
C.木块漂浮,$F_浮{}^\prime = G = 4\text{N}$,由$F_浮 = \rho _水gV_排$得,木块漂浮时排开水的体积:
$V_排{}^\prime = \frac {{F_浮{}^\prime}}{{\rho _水g}} = \frac {{4\text{N}}}{{1.0 \times {10}^3\text{kg/}\text{m}^3 \times 10\text{N/kg}}} = 4 \times 10^{- 4}\text{m}^3$,
$\Delta h = \frac {{\Delta V_排}}{S} = \frac {{1 \times {10}^{- 3}\text{m}^3 - 4 \times {10}^{- 4}\text{m}^3}}{{300 \times {10}^{- 4}\text{m}^2}} = 0.02\text{m}$,
则$\Delta P = \rho _水g\Delta h = 1.0 \times 10^3\text{kg/}\text{m}^3 \times 10\text{N/kg} \times 0.02\text{m} = 200\text{Pa}$,故C正确;
D.绳子断和断之前,容器对桌面的压力不变,受力面积不变,故剪断绳子待物块静止后水平地面受到的压强没有变化,故D错误.
故选BC.