The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that 45 percent of its volume is in oil while the rest is in water. The density of the body is_____kg/ $m^{3}$ .
The specific gravity of oil is 0.7 and density of water is 1000 kg/ $m^{3}$ .
Acceleration due to gravity: g=10 m/ $s^{2}$ .

865

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Solution

The correct option is A 865
Let V=Volume of metallic body
45% of volume is in oil
i.e.., $V_{o i l}$ = 45% of V
=0.45 V
and
$V_{w a t e r} = 0.55 V$

For equilibrium condition,
Net buoyant force = $(F_{B})_{w} + (F_{B})_{o i l}$
=Weight of body

$M_{b} g = ρ_{w} V_{w} g + ρ_{o i l} V_{o i l} g$

$M_{b} = ρ_{w} V_{w} + ρ_{o i l} V_{o i l}$

$ρ_{b} V = ρ_{w} \times 0.55 V + ρ_{o i l} \times 0.45 V$

or $ρ_{b} = ρ_{w} \times 0.55 + ρ_{o i l} \times 0.45$

$= 1000 \times 0.55 + 700 \times 0.45$

$= 550 + 315 = 865 k g / m^{3}$

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