Question

A vessel contains oil (density $0.8g/cc$) over mercury (density $13.6g/cc$). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $g/cc$ is:

• A. $3.3$
• B. $6.4$
  
• C. $7.2$
  
• D. $12.8$
  

Answer 1

Answer: (C)

$7.2$

The mass of sphere be $m$

$m=dv$ , where $d$ is density and $v$ is volume

So we have $m=M_o+m_m$

$\Rightarrow dv=d_o\times \frac{v}{2}+d_m\times \frac{v}{2}$

$\Rightarrow d=\frac{d_o+d_m}{2}$

$\Rightarrow d=\frac{0.8+13.6}{2}=7.2$

Therefore the correct option is $C$