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A sphere contracts to 0.01% volume, when...

A sphere contracts to 0.01% volume, when taken to the bottom of sea 1 km deep. Find the bulk modulus of the material of the sphere. Density of sea water = `1.0xx10^3 kg//m^3`.

Text Solution

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We are given:
`(Delta V)/(V)=(0.01)/(100), h= 1 km=10^3 m`
`rho=1.0xx10^3 kg m^(-3)`
We are to calculate: bulk modulus of the material, B.
Using relation: `p = h rho g = 10^3 xx 1.0 xx10^3 xx 9.8= 9.8xx10^6 N m^(-2)`,
We know that, `B=(p)/((Delta V)/(V))=(9.8 xx10^6xx100)/(0.01)= 9.8xx10^(10) N m^(-2)`
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