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Question: A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the...

A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball

A

19.6×108N/m219.6 \times 10^{8}N/m^{2}

B

19.6×10−10N/m219.6 \times 10^{- 10}N/m^{2}

C

19.6×1010N/m219.6 \times 10^{10}N/m^{2}

D

19.6×10−8N/m219.6 \times 10^{- 8}N/m^{2}

Answer

19.6×108N/m219.6 \times 10^{8}N/m^{2}

Explanation

Solution

K=PΔV/V=hdgΔV/V=200×103×9.80.001=19.6×108N/m2K = \frac{P}{\Delta V/V} = \frac{hdg}{\Delta V/V} = \frac{200 \times 10^{3} \times 9.8}{0.001}\mathbf{= 19.6}\mathbf{\times}\mathbf{1}\mathbf{0}^{\mathbf{8}}\mathbf{N/}\mathbf{m}^{\mathbf{2}}