Question

# A vessel contains oil (density $$0.8 g/cc$$) over mercury (density $$13.6 g/cc$$). 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

Solution

## The correct option is D $$7.2$$The mass of sphere be $$m$$$$m=dv$$ , where  $$d$$ is density and $$v$$ is volumeSo we have $$m=M_{o}+m_{m}$$$$\Rightarrow dv=d_{o} \times \dfrac{v}{2}+d_{m} \times \dfrac{v}{2}$$$$\Rightarrow d = \dfrac{d_{o}+d_{m}}{2}$$$$\Rightarrow d=\dfrac{0.8+13.6}{2}=7.2$$Therefore the correct option is $$C$$Physics

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