The approximate depth of an ocean is 2700 m. The compressibility of water is `45.4 xx 10 ^(-11) Pa ^(-1)` and density of water is `10 ^(3) kg//m^(3).` What fractional compression `(Delta V)/(V)` of water will be obtained at the bottom of the ocean? (Take `g = 10 ms ^(-2)`)

Options

A. `1.2 xx 10 ^(-2)`
B. `1.4 xx 10 ^(-2)`
C. `0.8 xx 10 ^(-2)`
D. `1.0 xx 10 ^(-2)`

Answer

A

Explanation

The excess pressure at the bottom of ocean
`Delta P = h rho g`
`= 2700 xx 10 ^(3) xx 10 `
`= 27 xx 10 ^(6) Pa`
Bulk modulus `B = | (Delta P )/((Delta V )/(V ))|`
`therefore (Delta V)/(V) = (Delta P)/(B)`
`= Delta PK[because (1)/(B) =K]`
`=45.4 xx 10 ^(-11) xx 27 xx 10 ^(6)`
`=1225.8 xx 10 ^(-5)`
`~~1.2 xx 10 ^(-2)`