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Question

A solid sphere of radius $$r$$ made of a material of bulk modulus $$B$$ is surrounded by a liquid in a liquid in a cylindrical container. A mass less piston of area a floats on the surface of the liquid. When a mass $$m$$ is placed on the piston compress the liquid, the fraction change in the radius of the sphere $$(dr/r)$$ is :


A
Ba/mg
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B
Ba/3mg
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C
mg/3Ba
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D
mg/Ba
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Solution

The correct option is C $$mg/3B a$$

$$\Delta P=\frac{m g}{a}$$

$$\frac{\Delta V}{V}=\frac{\Delta p}{B}$$

$$ \begin{aligned} v=\frac{4}{3} \pi g^{3} & \\ \frac{\Delta v}{v}=\frac{3 \Delta n}{r} \\ \frac{3 \Delta g}{r}=\frac{m g}{a \beta} \\ \frac{\Delta r}{r}=\frac{m g}{3 a \beta} \end{aligned} $$ 


Physics

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