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 of water will be obtained at the bottom of the ocean ?

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

Depth of ocean d= 2700m
Density of water `rho = 10^(3) kg m^(-3)`
Compressibility of water, `K= 45.4 xx 10^(-11) Pa^(-1)`
`(Delta V)/(V)` = ?
Excess pressure at the bottom `Delta P= rho gd`
`=10^(3) xx 10 xx 2700 = 27 xx 10^(6)Pa`
we know, `B= (Delta P)/((Delta V//V))`
`((Delta V)/(V)) = (Delta P)/(B) = K.Delta P ( :. K = (1)/(B))`
`=45.4 xx 10^(-11) xx 27 xx 10^(6) = 1.2 xx 10^(-2)`