Question
Physics Question on Hydrostatics
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?
A
776kg/m3
B
954kg/m3
C
1024kg/m3
D
1276kg/m3
Answer
954kg/m3
Explanation
Solution
Given,
Density of oil (ρ1)=724kg/m3
Density of water (ρ2)=1000kg/m3
According to Archemedes' principle,
Upthrust = Weight of the liquid displaced
Vρbg=V0ρ1g+Vwρ2g
(V0 and Vw are volume of oil and water displaced respectively)
Vρbg=6V(724)g+65V(1000)g
where, ρb= density of block
and V0=6V and Vw=65V
⇒Vρbg=(6724V+65000V)g
⇒Vbg=(6724V+5000V)g
⇒Vρbg=65724Vg
ρb=954kg/m3