(2011?闸北区一模)两个盛有不同液体的圆柱形容器A和B,底面积不同(SA<SB),有一个小球甲浸没在容器A

2025-03-13 08:35:53
推荐回答(1个)
回答1:

(1)∵hA=hB,SA<SB
液体对容器底部的压力相等;
根据公式p=
F
S
可知,F=pS=ρghS;
因为两容器中的液面高度相等,这时液体对容器底部的压力相等;又因为SA<SB,所以液体密度关系为ρA>ρB
(2)根据公式根据公式p=
F
S
可知,B容器受到液体的压强较小;
将两个小球分别从液体中取出后,两容器中液体对容器底部的压强相等; 根据F=pS,两个容器内液体对容器底的压强相等,底面积不相等,则FA<FB,A容器内液体对容器底的压力小于B容器内液体对容器底的压力,
(3)刚开始压力相等,高度相等,推出密度之比等于底面积的反比,拿出球以后,假设两球体积相等,那么两液体下降的高度和底面积成反比,根据压强相等列式
ρAg(h-hA)=ρBg(h-hB)   hA指A容器下降的液面高度,hB指B容器下降的液面高度
ρA
ρB
h?hA
h?hB
=
SB
SA
   推出 SA(h-hA)=SB(h-hB)  
即h(SA-SB)=SAhA-SBhB<0
该式中SAhA恰好代表A球的体积,SBhB恰好代表B球的体积,
所以甲球的体积小于乙球的体积.但无法判断俩两个小球排开的体积的大小,还不知道两球的密度关系,所以无法判断质量的关系,故ABC错误.
故选D.

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