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Question

# A vessel contains oil (density = 0.8 gm / cm3) Over mercury (density = 13.6 gm / cm3). 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 gm/cm3

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 the sphere = 43πR3ρg Upthrust due to oil and mercury= 23πR3×σoilg+23πR3σHgg.....(ii) Equating (i) and (ii) 43πR3ρg=23πR30.8g+23πR3×13.6g⇒2ρ=0.8+13.6=14.4⇒ρ=7.2

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