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Q.

A ball falling in a lake of depth 200 m shows a decrease of 0.1% in its volume at the bottom. The bulk modulus of the elasticity of the material of the ball is $(take g = 10 {ms}^{- 12})$

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a

$10^{9} N / m^{2}$

b

$2 \times 10^{9} N / m^{2}$

c

$4 \times 10^{9} N / m^{2}$

d

$3 \times 10^{9} N / m^{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} ΔP = hρg = 200 \times 10^{3} \times 10 N / m^{2} = 2 \times 10^{6} N / m^{2} \\ K = \frac{ΔP}{\frac{ΔV}{V}} = \frac{2 \times 10^{6}}{\frac{0 .1}{100}} = \frac{2 \times 10^{8}}{0 .1} N / m^{2} = 2 \times 10^{9} N / m^{2} \end{array}$

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