A solid rectangular block measures 0.1m by 0.08m by 0.06m and floats freely in a liquid of density 13546kg/m3. If the depth of the liquid is 0.045m up to the block's largest side. Find the density of the block?
mg=FAmg=F_Amg=FA
ρVg=ρlVlg\rho Vg=\rho_l V_l gρVg=ρlVlg
ρV=ρlVl\rho V= \rho_l V_lρV=ρlVl
ρhS=ρlhlS\rho h S=\rho_l h_l SρhS=ρlhlS
ρh=ρlhl\rho h=\rho_l h_lρh=ρlhl
ρ=ρlhlh=13546⋅0.0450.1=6096 kgm3\rho=\rho_l \frac{h_l}{h}=13546\cdot \frac{0.045}{0.1}=6096 ~\frac{kg}{m^3}ρ=ρlhhl=13546⋅0.10.045=6096 m3kg
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