SATHEE: Properties Of Solids And Liquids Question 193

Properties Of Solids And Liquids Question 193

Question: A vessel contains oil (density = 0.8 gm/cm3) over mercury (density = 13.6 gm/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 gm/cm3 is[IIT-JEE 1988]

Options:

A) 3.3

B) 6.4

C) 7.2

D) 12.8

Show Answer

Answer:

Correct Answer: C

Solution:

As the sphere floats in the liquid.

Therefore its weight will be equal to the upthrust force on it Weight of sphere $= \frac{4}{3} π R^{3} ρ g$ .(i)

Upthrust due to oil and mercury $= \frac{2}{3} π R^{3} \times σ_{o i l} g + \frac{2}{3} π R^{3} σ_{H g} g$ .(ii)

Equating (i) and (ii) $\frac{4}{3} π R^{3} ρ g = \frac{2}{3} π R^{3} 0.8 g + \frac{2}{3} π R^{3} \times 13.6 g$

$\Rightarrow 2 ρ = 0.8 + 13.6 = 14.4 \Rightarrow ρ = 7.2$

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Properties Of Solids And Liquids Question 193

Question: A vessel contains oil (density = 0.8 gm/cm3) over mercury (density = 13.6 gm/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 gm/cm3 is[IIT-JEE 1988]

Options:

Answer:

Solution:

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