Question

Please solve question 149?

Answer 1

`"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)`

Answer 2

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)"`