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Question Number 227868 by mr W last updated on 22/Feb/26

Commented by mr W last updated on 22/Feb/26

As shown in the figure in a beaker on a horizontal table containing some salt water an ice block A is floating and an object B is suspended in the liquid. After the ice block A melts completely, which of the following statements is/are correct? A. The density of the salt water in the beaker decreases. B. The liquid level in the beaker does not change. C. The pressure exerted by the liquid on the bottom of the beaker decreases. D. The buoyant force acting on the object B decreases.

$$\mathrm{As}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{in}\:\mathrm{a}\:\mathrm{beaker}\:\mathrm{on}\: \\ $$$$\mathrm{a}\:\mathrm{horizontal}\:\mathrm{table}\:\mathrm{containing}\:\mathrm{some} \\ $$$$\mathrm{salt}\:\mathrm{water}\:\mathrm{an}\:\mathrm{ice}\:\mathrm{block}\:\mathrm{A}\:\mathrm{is}\:\mathrm{floating}\: \\ $$$$\mathrm{and}\:\mathrm{an}\:\mathrm{object}\:\mathrm{B}\:\mathrm{is}\:\mathrm{suspended}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{liquid}.\:\mathrm{After}\:\mathrm{the}\:\mathrm{ice}\:\mathrm{block}\:\mathrm{A}\:\mathrm{melts} \\ $$$$\mathrm{completely},\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{statements}\:\mathrm{is}/\mathrm{are}\:\mathrm{correct}? \\ $$$$\mathrm{A}.\:\mathrm{The}\:\mathrm{density}\:\mathrm{of}\:\mathrm{the}\:\mathrm{salt}\:\mathrm{water}\:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{beaker}\:\mathrm{decreases}. \\ $$$$\mathrm{B}.\:\mathrm{The}\:\mathrm{liquid}\:\mathrm{level}\:\mathrm{in}\:\mathrm{the}\:\mathrm{beaker}\: \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{change}. \\ $$$$\mathrm{C}.\:\mathrm{The}\:\mathrm{pressure}\:\mathrm{exerted}\:\mathrm{by}\:\mathrm{the}\:\mathrm{liquid} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{the}\:\mathrm{beaker}\:\mathrm{decreases}. \\ $$$$\mathrm{D}.\:\mathrm{The}\:\mathrm{buoyant}\:\mathrm{force}\:\mathrm{acting}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{object}\:\mathrm{B}\:\mathrm{decreases}. \\ $$

Answered by mr W last updated on 23/Feb/26

Commented by mr W last updated on 23/Feb/26

ρ_B =ρ_s V_(i1) ρ_s =(V_(i1) +V_(i2) )ρ_i =V_(iw) ρ_w V_s ′=V_s +V_(iw) =V_s +(ρ_s /ρ_w )V_(i1) >V_s +V_(i1) ⇒h′>h ρ_(s′) =((V_s ρ_s +V_(i1) ρ_s )/(V_s ′))=(((V_s +V_(i1) )ρ_s )/(V_s +(ρ_s /ρ_w )V_(i1) ))<ρ_s

$$\rho_{{B}} =\rho_{{s}} \\ $$$${V}_{{i}\mathrm{1}} \rho_{{s}} =\left({V}_{{i}\mathrm{1}} +{V}_{{i}\mathrm{2}} \right)\rho_{{i}} ={V}_{{iw}} \rho_{{w}} \\ $$$${V}_{{s}} '={V}_{{s}} +{V}_{{iw}} ={V}_{{s}} +\frac{\rho_{{s}} }{\rho_{{w}} }{V}_{{i}\mathrm{1}} >{V}_{{s}} +{V}_{{i}\mathrm{1}} \\ $$$$\Rightarrow{h}'>{h} \\ $$$$\rho_{{s}'} =\frac{{V}_{{s}} \rho_{{s}} +{V}_{{i}\mathrm{1}} \rho_{{s}} }{{V}_{{s}} '}=\frac{\left({V}_{{s}} +{V}_{{i}\mathrm{1}} \right)\rho_{{s}} }{{V}_{{s}} +\frac{\rho_{{s}} }{\rho_{{w}} }{V}_{{i}\mathrm{1}} }<\rho_{{s}} \\ $$

Commented by mr W last updated on 23/Feb/26

A is correct B is wrong C is correct D is correct

$${A}\:{is}\:{correct} \\ $$$${B}\:{is}\:{wrong} \\ $$$${C}\:{is}\:{correct} \\ $$$${D}\:{is}\:{correct} \\ $$

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