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Question

# A vessel contains oil (density = 0.8 g/cm3) over mercury (density = 13.6 g/cm3). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in g/cm3 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 C 7.2 As the sphere floats in the liquid, therefore its weight will be equal to the upthrust force on it. Weight of sphere = 43πR3ρg.......(i) Upthrust due to oil and mercury, =23πR3ρoilg+23πR3ρHgg......(ii) Equating (i) and (ii), 43πR3ρg=23πR3(0.8)g+23πR3(13.6)g ⇒2ρ=0.8+13.6=14.4⇒ρ=7.2 g/cm3

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