Question

A metallic sphere floats in an immiscible mixture of water $(p_w={10}^{3}kg/m^3)$ and a liquid $(p_L=13.5\times {10}^3)$ with (1/5)th portion by volume in the liquid and remaining in the water. The density of the metal is

• A. $4.5\times {10}^{3}kg/m^3$
• B. $4.0\times {10}^{3}kg/m^3$
• C. $3.5\times {10}^{3}kg/m^3$
• D. $1.9\times {10}^{3}kg/m^3$

Answer 1

Answer: (C)

$3.5\times {10}^{3}kg/m^3$

Since the metallic sphere rest in the liquid mixture the gravitational force is balanced by buoyant force.
weight of metallic sphere $=$ weight of liquid 1 + weight of liquid 2
let V be volume of sphere,
$mg=m_{1}g+m_{2}g$
$V\rho g=\frac{4V}{5}\times {10}^{3}g+\frac{V}{5}\times 13.5\times {10}^{3}g\rho =3.5\times {10}^{3}kg/m^3$