Please solve question 149?

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2 Answers
Apr 7, 2018

#"3)"(rho_1 - ρ)/(rho_1 - rho_2)#

Explanation:

Volume of ball = Volume of liquids displaced

#"V" = "V"_1 + "V"_2 color(white)(...)……(1)#

Weight of ball = Weight of #2# liquids of volume #"V"_1# and #"V"_2#

#"mg = m"_1"g" + "m"_2"g"#

#"m = m"_1 + "m"_2#

#"Vρ" = "V"_1 "ρ"_1 + "V"_2"ρ"_2 color(white)(...)[∵ "Mass = Volume × Density"]#

#"Vρ" = ("V - V"_2)"ρ"_1 + "V"_2"ρ"_2 color(white)(..)[∵ "from"\ (1)]#

#"Vρ" = "V"ρ_1 - "V"_2ρ_1 + "V"_2rho_2#

#"V"_2(ρ_1 - ρ_2) = "V"(ρ_1 - ρ)#

#"V"_2/"V" = (rho_1 - ρ)/(rho_1 - rho_2)#

Apr 7, 2018

The answer is #"option (3)"#

Explanation:

According to Archimedes ' principle

#"weight of the immersed body "=" weight of fluid displaced"#

Let the volume of the upper part be #=V_1#

The weight of fluid displaced is #=rho_1V_1g#

Let the volume of the lower part be #=V_2#

The weight of fluid displaced is #=rho_2V_2g#

The weight of the ball is #=rho(V_1+V_2)g#

Therefore,

#rho_1V_1g+rho_2V_2g=rho(V_1+V_2)g#

#rho_1V_1+rho_2V_2=rho(V_1+V_2)#

The fraction is #=V_2/(V_1+V_2)#

Let, #V=V_1+V_2#

Therefore,

#rho_1(V-V_2)+rho_2V_2=rho(V)#

#rho_1V-rho_1V_2+rho_2V_2=rho(V)#

#rho_1V-rhoV=rho_1V_2-rho_2V_2#

#V_2/V=(rho_1-rho)/(rho_1-rho_2)#

The answer is #"option (3)"#