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Question

A body floats in water with one fourth of its volume above the surface of water. If placed in oil it floats with one third of its volume above the surface of oil. The density of oil is?


A
34
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B
49
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C
23
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D
98
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Solution

The correct option is C $$\displaystyle\frac{9}{8}$$
The volume of body above water is one -fourth. So the volume inside the water will be $$\dfrac34\ th$$ of its volume.

Let the volume of the body be V and density be $$d$$ . Then for the case of water 

$$V\times d\times g=\displaystyle\frac{3}{4}\times V\times d_{water}\times g$$
Now, for oil
The one-third of body is above oil so, the volume of body present in oil is $$\dfrac23\ rd$$ of its volume
 $$V\times d\times g=\displaystyle\frac{2}{3}\times V\times d_{oil}\times g$$

Therefore, 
$$\Rightarrow \displaystyle\frac{d_{oil}}{d_{water}}=\frac{9}{8}$$.

Physics

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