Properties of Matter 2 Question 7
7. A vessel contains oil (density $=0.8 g / cm^{3}$ ) over mercury (density $\left.=13.6 g / cm^{3}\right)$. 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 $g / cm^{3}$ is
(a) 3.3
(b) 6.4
(c) 7.2
(d) 12.8
(1988, 2M)
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Answer:
Correct Answer: 7. (c)
Solution:
- Let density of material of sphere (in $g / cm^{3}$ ) be $\rho$.
Applying the condition of floatation,
Weight $=$ Upthrust
or
$$ \begin{aligned} V \rho g & =\frac{V}{2} \rho _{\text {oil }} g+\frac{V}{2} \rho _{Hg} g \\ \rho & =\frac{\rho _{\text {oil }}}{2}+\frac{\rho _{Hg}}{2} \\ & =\frac{0.8}{2}+\frac{13.6}{2}=7.2 g / cm^{3} \end{aligned} $$
$$ \text { or } \quad \rho=\frac{\rho _{\text {oil }}}{2}+\frac{\rho _{Hg}}{2} $$
