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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
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B
6.4
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C
7.2
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D
12.8
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Solution

The correct option is D $$7.2$$

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

Physics

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