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A solid sphere of radius 2cm of bulk modulus $2\times 10^6N/m^2$ is surrounded by a liquid in cylindrical container.A massless piston of area $100cm^2$ floats on the surface of the liquid.When a mass 30Kg is placed on piston to compress the liquid what is fractional change in the radius of sphere

$\begin{array}{1 1}(A)\;2\%\\(B)\;.5\%\\(C)\;1\%\\(D)\;3\%\end{array} $

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As $V=\large\frac{4}{3}$$\pi R^3$
$\large\frac{\Delta V}{V}=\frac{3\Delta R}{R}$
$B=\large\frac{P}{\Delta V/V}$
$\;\;\;=\large\frac{30\times 9.8}{10^2\times 10^{-4}}$
$\;\;\;=3\times 9.8\times 10^3N/m^2$
$\large\frac{\Delta V}{V}=\frac{P}{B}$
$\Rightarrow \large\frac{3\times 9.8\times 10^3}{2\times 10^6}$
$\Rightarrow 1.47\times 10^{-2}$
$\large\frac{\Delta R}{R}=\frac{1}{3}\frac{\Delta V}{V}$
$\Rightarrow .49\times 10^{-2}$
$\Rightarrow .49\%$
$\Rightarrow \approx .5\%$
Hence (B) is the correct answer.
answered May 8, 2014 by sreemathi.v

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