A block of wood floats in freshwater with two-third of its volume submerged. In oil, the block floats with one-fourth of its volume submerged. The density of oil is

Question

A block of wood floats in freshwater with two-third of its volume submerged. In oil, the block floats with one-fourth of its volume submerged. The density of oil is (A) 2666.7 kgm- 3 (B) 5333.3 kgm- 3 (C) 1333.3 kgm- 3 (D) 3333.3 kgm- 3

Tardigrade Admin · Accepted Answer

ρ w (2/3) V=ρ bV ρ o i l (1/4) V=ρ bV ∴ (2/3) ρ w=(1/4) ρ o i l ρ o i l=(8/3) ρ w =(8000/3)=2666.7

Q. A block of wood floats in freshwater with two-third of its volume submerged. In oil, the block floats with one-fourth of its volume submerged. The density of oil is

$2666.7 k g m^{- 3}$

$5333.3 k g m^{- 3}$

$1333.3 k g m^{- 3}$

$3333.3 k g m^{- 3}$

$ρ_{w} \frac{2}{3} V = ρ_{b} V$
$ρ_{o i l} \frac{1}{4} V = ρ_{b} V$
$∴ \frac{2}{3} ρ_{w} = \frac{1}{4} ρ_{o i l}$
$ρ_{o i l} = \frac{8}{3} ρ_{w}$
$= \frac{8000}{3} = 2666.7$

Q. A block of wood floats in freshwater with two-third of its volume submerged. In oil, the block floats with one-fourth of its volume submerged. The density of oil is

2666.7kgm−3

5333.3kgm−3

1333.3kgm−3

3333.3kgm−3

ρw​32​V=ρb​V ρoil​41​V=ρb​V ∴32​ρw​=41​ρoil​ ρoil​=38​ρw​ =38000​=2666.7

$2666.7 k g m^{- 3}$

$5333.3 k g m^{- 3}$

$1333.3 k g m^{- 3}$

$3333.3 k g m^{- 3}$

$ρ_{w} \frac{2}{3} V = ρ_{b} V$
$ρ_{o i l} \frac{1}{4} V = ρ_{b} V$
$∴ \frac{2}{3} ρ_{w} = \frac{1}{4} ρ_{o i l}$
$ρ_{o i l} = \frac{8}{3} ρ_{w}$
$= \frac{8000}{3} = 2666.7$