A layer of oil with density 724 kg/m3 floats on water of density 1000 kg/m3. A block floats at the oil-water interface with 1/6 of its volume in oil and 5/6 of its volume in water, as shown in the figure. What is the density of the block?

Question

A layer of oil with density 724 kg/m3 floats on water of density 1000 kg/m3. A block floats at the oil-water interface with 1/6 of its volume in oil and 5/6 of its volume in water, as shown in the figure. What is the density of the block? (A) 776 kg/m3 (B) 954 kg/m3 (C) 1024 kg/m3 (D) 1276 kg/m3

Tardigrade Admin · Accepted Answer

Given, Density of oil (ρ1)=724 kg / m 3 Density of water (ρ2)=1000 kg / m 3 According to Archemedes' principle, Upthrust = Weight of the liquid displaced V ρb g=V0 ρ1 g +Vw ρ2 g (V0. and Vw are volume of oil and water displaced respectively) V ρb g=(V/6)(724) g+(5 V/6)(1000) g where, ρb= density of block and V0 =(V/6) and Vw=(5 V/6) ⇒ V ρb g =((724 V/6)+(5000 V/6)) g ⇒ Vb g =((724 V+5000 V/6)) g ⇒ V ρb g =(5724/6) V g ρb =954 kg / m 3

Q. A layer of oil with density $724 k g / m^{3}$ floats on water of density $1000 k g / m^{3}$ . A block floats at the oil-water interface with $1/6$ of its volume in oil and $5/6$ of its volume in water, as shown in the figure. What is the density of the block?

$776 k g / m^{3}$

$954 k g / m^{3}$

$1024 k g / m^{3}$

$1276 k g / m^{3}$

Q. A layer of oil with density 724kg/m3 floats on water of density 1000kg/m3. A block floats at the oil-water interface with 1/6 of its volume in oil and 5/6 of its volume in water, as shown in the figure. What is the density of the block?

776kg/m3

954kg/m3

1024kg/m3

1276kg/m3

Q. A layer of oil with density $724 k g / m^{3}$ floats on water of density $1000 k g / m^{3}$ . A block floats at the oil-water interface with $1/6$ of its volume in oil and $5/6$ of its volume in water, as shown in the figure. What is the density of the block?

$776 k g / m^{3}$

$954 k g / m^{3}$

$1024 k g / m^{3}$

$1276 k g / m^{3}$