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17 Shijingshan mathematical model 2
∫ Cubic side length LB=2LA,

∴VA:VB=(LA)3:(LB)3= 1:8,

Bottom area ratio:

SA:SB=(LA)2:(LB)2= 1:4,

∫G = mg =ρVg, AB density is the same,

∴ ga: GB = ρ vag :ρvbg = va: VB =1:8, so b is wrong;

∫p = FS = GS,

∴ Pa: Pb = GASA: GBSB =11:84 =1:2, so d is wrong;

η A =GAh? (GA+? G move) h=GAGA+G move,

ηB = GBh(G b+ G move)h = GBGB+G move = 8G8GA+G move

√ηA:ηB = 4 1:48,

That is Gaga+gmove: 8Ga+gmove = 41:48,

Simplify:

Ga: g move = 5: 1,

∴ GB: G = 40: 1, so C is wrong;

When a rises at a constant speed in the water,

η=(GA? F floating) h? (GA? F floating+? G moving) h

=GA? F floating GA? F floating +G moving

=GA? F floating GA? F floating+15GA

=GA? F floating 65GA? F floating

=ρAVAgρ water VAg65ρAVAgρ water VAg=80%,

Solution: ρA=5× 103kg/m3, so A is correct.

So choose a.