A vessel contains oil (density $= 0.8 g m / c m^{3})$ over mercury (density $= 13.6 g m / c m^{3})$ . A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in $g m / c m^{3}$ is

3.3

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6.4

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7.2

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12.8

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Solution

The correct option is B $7.2$
A vessel contains oil density $= 0.8 g m / c m^{3}$
Mercury density $= 13.6 g m / c m^{3}$
Total weight is balanced by the displaced volumes of the two different fluids. Let it $s$ and volume id $v$ and te density is $n$ .
Then the equilibrium condition should be
$v_{m g} = v / 2 (0.8) g + \frac{v}{2 \times 136 g} n = 0.4 + 6.8 = 7.2 g m / c m^{3}$

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Similar questions

Q. A vessel contains oil (density = 0.8

g m / c m^{3}

) over mercury (density = 13.6

g m / c m^{3}

). A uniform sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of sphere in

g m / c m^{3}

is:

A vessel contains oil (density = 0.8 gm / $c m^{3}$ ) Over mercury (density = 13.6 gm / $c m^{3}$ ). 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/ $c m^{3}$